Updated on 2025/05/30

写真a

 
Yamauchi Takamitsu
 
Organization
Graduate School of Science and Engineering (Science) Major of Science and Engineering Mathematics and Computer Science Professor
Title
Professor
Contact information
メールアドレス
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Degree

  • Doctor of Science ( 2006.3   University of Tsukuba )

  • Master of Science ( 2003.3   University of Tsukuba )

Research Interests

  • topological space

  • dimension theory

  • metirc space

  • general topology

  • continuous selection

Research Areas

  • Natural Science / Geometry

Education

  • University of Tsukuba   Graduate School of Pure and Applied Sciences   Doctoral Program of Mathematics

    2001.4 - 2006.3

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    Country： Japan

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  • University of Tsukuba   First Cluster of College   College of Natural Science

    1997.4 - 2001.3

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    Country： Japan

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Research History

  • Graduate School of Science and Engineering, Ehime University   Professor

    2020.10

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  • Graduate School of Science and Engineering, Ehime University   Associate Professor

    2014.4 - 2020.9

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  • Interdisciplinary Graduate School of Science and Engineering, Shimane University   Lecturer

    2012.4 - 2014.3

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  • Interdisciplinary Faculty of Science and Engineering, Shimane University   Lecturer

    2009.4 - 2012.3

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  • Department of General Education, Kure National College of Technology   Lecturer

    2008.4 - 2009.3

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  • Interdisciplinary Faculty of Science and Engineering, Shimane University   Teaching Associate

    2005.4 - 2008.3

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Professional Memberships

  • The Mathematical Society of Japan

    2005.4

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Papers

  • Coarse compactifications and controlled products Reviewed

    Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi

    Journal of Topology and Analysis   14 ( 04 )   875 - 900   2022.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

    We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space is the ideal boundary of a coarse compactification of the space. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications.

    DOI： 10.1142/s1793525321500102

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  • Coarse infinite-dimensionality of hyperspaces of finite subsets Reviewed

    Thomas Weighill, Takamitsu Yamauchi, Nicolò Zava

    European Journal of Mathematics   8 ( 1 )   335 - 355   2022.3

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    Language：English   Publishing type：Research paper (scientific journal)  

    We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property.

    DOI： 10.1007/s40879-021-00515-3

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  • Connectedness properties of the Higson corona of the half line Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   301   107542 - 26pp   2021.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    It is proved that the Higson corona of the half line satisfies the following connectedness properties: The Higson corona of the half line is hereditarily unicoherent; under the Continuum Hypothesis, there are 2c composants of the Higson corona of the half line; the principle of Near Coherence Filters is equivalent to the assertion that the Higson corona of the half line has only one composant; no non-degenerate subcontinuum of the Higson corona of the half line is hereditarily indecomposable; and every non-empty open subset of the Higson corona of the half line contains a non-degenerate indecomposable continuum.

    DOI： 10.1016/j.topol.2020.107542

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  • Transfinite asymptotic dimension and APD profiles Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   295   107675 - 7pp   2021.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We prove that for a positive integer m and a non-negative integer n, if the transfinite asymptotic dimension of an ∞-pseudometric space X is at most m⋅ω+n, then X has an integral APD profile (n+1,α1,…,αm) for some non-decreasing functions α1,…,αm. This answers a question of Orzechowski posed in 2020.

    DOI： 10.1016/j.topol.2021.107675

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  • Higson compactifications of Wallman type Reviewed

    Yasser F. Ortiz-Castillo, Artur Hideyuki Tomita, Takamitsu Yamauchi

    Tsukuba Journal of Mathematics   42 ( 2 )   233 - 250   2018.12

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.21099/tkbjm/1554170423

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  • Linear extension operators of bounded norms Reviewed

    Dmitri Shakhmatov, Vesko Valov, Takamitsu Yamauchi

    Journal of Mathematical Analysis and Applications   466 ( 1 )   952 - 960   2018.10

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    Dugundji spaces were introduced by Pełczyński as compact Hausdorff spaces X such that every embedding of X into a Tychonoff cube [0,1]A admits a linear extension operator u:C(X)→C([0,1]A) such that ‖u‖=1 and u(1X)=1[0,1]A, where 1X is the constant function on X taking value 1. In this paper we show that a compact space X is Dugundji provided that there exists a linear extension operator u:C(X)→C([0,1]A) satisfying one of the following conditions: (a) ‖u‖<2 and |u(f⋅g)|≤‖g‖⋅|u(|f|)| for all f,g∈C(X);(b) ‖u‖=1.

    DOI： 10.1016/j.jmaa.2018.06.030

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  • Another proof of a theorem of van Mill and Wattel on weak selections Reviewed

    Koichi Motooka, Takamitsu Yamauchi

    Colloquium Mathematicum   152 ( 2 )   165 - 174   2018

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    Publishing type：Research paper (scientific journal)   Publisher：Institute of Mathematics, Polish Academy of Sciences  

    We give another proof of the following theorem due to van Mill and Wattel: If a Hausdorff space has a locally uniform weak selection, then it is a generalized ordered space. A characterization of weak orderability in terms of weak selections is also given.

    DOI： 10.4064/cm7214-9-2017

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  • The existence of continuous weak selections and orderability-type properties in products and filter spaces Reviewed

    Koichi Motooka, Dmitri Shakhmatov, Takamitsu Yamauchi

    Topology and its Applications   232   45 - 60   2017.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    Orderability, weak orderability and the existence of continuous weak selections on spaces with a single non-isolated point and their products are discussed. We prove that a closed continuous image X of a suborderable space must be hereditarily paracompact provided that its product X x Y with some non-discrete space Y has a separately continuous weak selection. (C) 2017 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2017.09.030

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  • Straight finite decomposition complexity implies property A for coarse spaces Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   231   329 - 336   2017.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    It is proved that straight finite coarse decomposition complexity implies coarse property A, where straight finite coarse decomposition complexity and coarse property A are generalizations of straight finite decomposition complexity and property A to the case of coarse spaces, respectively. This answers a question of Bell, Moran and Nagorko. (C) 2017 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2017.09.034

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  • On pseudocompact spaces with a weak selection Reviewed

    Dikran Dikranjan, Kazumi Miyazaki, Tsugunori Nogura, Takamitsu Yamauchi

    Topology and its Applications   230   490 - 505   2017.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We study properties of the pseudocompact spaces X with a weak selection, and we dedicate a particular attention to the weak selection topologies on X. In case when X is also locally compact, we obtain a convenient decomposition of X into a finite union of clopen sets, which are either almost compact or connected with a remainder of size two in their Stone-Cech compactification. (C) 2017 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2017.08.019

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  • Hereditarily infinite-dimensional property for asymptotic dimension and graphs with large girth Reviewed

    Takamitsu Yamauchi

    Fundamenta Mathematicae   236 ( 2 )   187 - 192   2017

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN  

    It is shown that every subspace of a coarse disjoint union of a sequence of graphs with large girth has infinite asymptotic dimension or asymptotic dimension at most one.

    DOI： 10.4064/fm266-6-2016

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  • Insertion theorems for maps to linearly ordered topological spaces Reviewed

    S. García-Ferreira, Y. F. Ortiz-Castillo, T. Yamauchi

    Topology and its Applications   188   74 - 81   2015.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    Let X be a topological space and (Y, &lt;=) a linearly ordered topological space. Following the Katetov-Tong Insertion Theorem, a pair (X, Y) is said to have the insertion property if for every upper semicontinuous map g : X -&gt; Y and every lower semicontinuous map h : X -&gt; Y with g(x) &lt;= h(x) for all x is an element of X, there exists a continuous map f : X -&gt; Y such that g(x) &lt;= f (x) &lt;= h(x) for all x is an element of X. We show that if (X, Y) has the insertion property for every normal space X, then Y is order isomorphic to some interval in the real line. We also prove that if X is a paracompact space or a cardinal and L is the double edged long line, then (X, L) has the insertion property. (C) 2015 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2015.03.011

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  • Asymptotic property C of the countable direct sum of the integers Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   184   50 - 53   2015.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    It is proved that the countable direct sum of the integers with a proper invariant metric has asymptotic property C, which answers a question posed by A. Dranishnikov and M. Zarichnyi. (C) 2015 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2015.01.013

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  • C<inf>0</inf> Coarse structures on uniform spaces Reviewed

    Kotaro Mine, Atsushi Yamashita, Takamitsu Yamauchi

    Houston Journal of Mathematics   41 ( 4 )   1351 - 1358   2015

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV HOUSTON  

    The definition of Co coarse structure introduced by Wright is extended to uniform spaces. It is proved that every topological coarse structure of a locally compact Hausdorff space is the Co coarse structure associated to some uniformity compatible with its topology.

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  • Continuous selections for proximal continuous paraconvex-valued mappings Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   169   45 - 50   2014.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We show that every metric-proximal continuous paraconvex- and closed-valued mapping from an arbitrary topological space into a Banach space admits a continuous selection, which answers a question of Gutsy. To show the result, we apply the selection factorization property introduced by Nedev. (C) 2014 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2014.02.031

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  • Factorising lower semi-continuous mappings Reviewed

    Valentin Gutev, Takamitsu Yamauchi

    Houston Journal of Mathematics   40 ( 3 )   969 - 986   2014

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV HOUSTON  

    In this paper, we deal with factorisations of lower semi-continuous mappings through metrizable spaces. Every metrizable space has a a-discrete base for its topology, i.e. for the family of its open sets. One of our main results is that a lower semi-continuous mapping from a space X to the nonempty closed subsets of a metrizable space Y can be factorised through a metrizable domain if and only if the pre-image of the topology of Y has a a-discrete base of cozero-sets. Several special cases are considered, also several applications are presented.

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  • On a simultaneous selection theorem Reviewed

    Takamitsu Yamauchi

    Studia Mathematica   215 ( 1 )   1 - 9   2013

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：POLISH ACAD SCIENCES INST MATHEMATICS  

    Valov proved a general version of Arvanitakis's simultaneous selection theorem which is a common generalization of both Michael's selection theorem and Dugundji's extension theorem. We show that Valov's theorem can be extended by applying an argument by means of Pettis integrals due to Repovs, Semenov and Shchepin.

    DOI： 10.4064/sm215-1-1

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  • Factorising usco mappings Reviewed

    Valentin Gutev, Takamitsu Yamauchi

    Topology and its Applications   159 ( 9 )   2423 - 2433   2012.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We deal with factorisations through metrizable spaces of compact-valued u.s.c. mappings. In case the domain has some higher separation axioms, we found some natural relationship with the graph of such mappings. For an arbitrary domain, we related such factorisations to compact-valued continuous expansions. (C) 2012 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2011.11.061

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  • Continuous selections for set-valued mappings with finite-dimensional convex values Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   159 ( 4 )   1219 - 1222   2012.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We show selection theorems for set-valued mappings with finite-dimensional convex values, one of which is a partial extension of a selection theorem due to S. Barov (2008) [1]. (C) 2011 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2011.11.007

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  • Strong paracompactness and multi-selections Reviewed

    Valentin Gutev, Takamitsu Yamauchi

    Topology and its Applications   157 ( 8 )   1430 - 1438   2010.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We characterize strong paracompactness in terms of usco multi-selections for closed-valued lower semi-continuous mappings into completely metrizable spaces, thus generalizing recent results obtained by Choban, Mihaylova and Nedev [M Choban, E Mihaylova, S Nedev, On selections and classes of spaces, Topology Appl 155 (2008) 797-804] Related results and applications are achieved as well (C) 2009 Elsevier B V All rights reserved

    DOI： 10.1016/j.topol.2009.06.017

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  • Continuous selections avoiding extreme points Reviewed

    Takamitsu Yamauchi

    Topology and its Applications   155 ( 8 )   916 - 922   2008.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    It is shown that if X is a countably paracompact collectionwise normal space, Y is a Banach space and phi : X -&gt; 2(Y) is a lower semicontinuous mapping such that phi(x) is Y or a compact convex subset with Card phi(x) &gt; 1 for each X epsilon X, then phi admits a continuous selection f : X -&gt; Y such that f (x) is not an extreme point of phi(x) for each X E X. This is an affirmative answer to the problem posed by V. Gutev, H. Ohta and K. Yamazaki [V. Gutev, H. Ohta and K. Yamazaki, Selections and sandwich-like properties via semi-continuous Banach-valued functions, J. Math. Soc. Japan 55 (2003) 499-521]. (c) 2007 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.topol.2007.02.016

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  • The role of countable paracompactness for continuous selections avoiding extreme points Reviewed

    Takamitsu Yamauchi

    Tsukuba Journal of Mathematics   32 ( 2 )   277 - 290   2008

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Mathematics, University of Tsukuba  

    DOI： 10.21099/tkbjm/1496165229

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  • Characterizations of some classes of perfect spaces in terms of continuous selections avoiding supporting sets Reviewed

    Takamitsu Yamauchi

    Bulletin of the Polish Academy of Sciences, Mathematics   56 ( 2 )   93 - 104   2008

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.4064/ba56-2-6

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  • AN INVERSE OF THE BERGE MAXIMUM THEOREM FOR INFINITE DIMENSIONAL SPACES Reviewed

    Takamitsu Yamauchi

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   9 ( 2 )   161 - 167   2008

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：YOKOHAMA PUBL  

    An inverse of the Berge maximum theorem for paracompact domains and locally convex topological vector space ranges is proved. Cellina&apos;s approximate selection theorem for paracompact domains and locally convex topological vector space ranges is also obtained.

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  • A characterization of metrizable finitistic spaces and its applications to upper semicontinuous set-valued selections Reviewed

    Takamitsu Yamauchi

    Houston Journal of Mathematics   33 ( 3 )   735 - 751   2007

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV HOUSTON  

    In this paper, we give two types of characterizations of finitistic spaces. One is in terms of perfect mappings from zero-dimensional metric spaces, which is analogous to K. Morita's characterization of finite-dimensional metrizable spaces. Another is by means of upper semicontinuous set-valued selections, which is an analogue of M. M. Coban's characterization of finite-dimensional paracompact spaces. Characterizations of some classes of infinite-dimensional spaces and a generalization of finitistic spaces will also be given.

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  • Continuous selections of simplex-valued mappings Reviewed

    Takamitsu Yamauchi

    Scientiae Mathematicae Japonicae   63 ( 2 )   183 - 189   2006

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  • On a selection theorem of Blum and Swaminathan Reviewed

    Takamitsu Yamauchi

    Commentationes Mathematicae Universitatis Carolinae   45 ( 4 )   681 - 691   2004

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    Language：English   Publishing type：Research paper (scientific journal)  

    Blum and Swaminathan [Pacific J. Math. 93 (1981), 251-260] introduced the notion of B-fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.

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MISC

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Presentations

  • On equivariant asymptotic dimension Invited

    山内貴光

    RIMS共同研究「作用素環と関係する群論とその周辺」  2025.1 

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    Event date： 2025.1

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：京都大学数理解析研究所   Country：Japan  

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  • On a characterization of equivariant asymptotic dimension

    山内貴光

    2024 早稲田幾何学的トポロジー研究集会  2024.3 

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    Event date： 2024.3

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：早稲田大学西早稲田キャンパス   Country：Japan  

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  • On dynamic asymptotic dimension of Stone-Čech extensions of proper cocomopact actions

    Takamitsu Yamauchi

    2023.12 

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    Event date： 2023.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Group coarse structures on locally compact abelian groups Invited International conference

    YAMAUCHI Takamitsu

    Mini-symposium ``Topology and Applications'' in Mathematics Days in Sofia  2023.7 

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    Event date： 2023.7

    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Group coarse structures on locally compact abelian groups

    Takamitsu Yamauchi

    General Topology Symposium 2022  2022.12 

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    Event date： 2022.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Coarse infinite-dimensionality of hyperspaces of finite subsets

    Takamitsu Yamauchi

    RIMS symposium "Set-Theoretic and Geometric Topology, and their applications to related fields"  2022.6 

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    Event date： 2022.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On transfinite asymptotic dimension

    Takamitsu Yamauchi

    RIMS symposium "Research Trends on General Topology and its Related Fields"  2021.6 

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    Event date： 2021.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 半直線のHigson coronaの連結性について

    山内貴光

    2019年度ジェネラルトポロジーシンポジウム  2019.12 

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    Event date： 2019.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Connectedness properties of the Higson corona of the half line Invited International conference

    YAMAUCHI Takamitsu

    The Third Pan-Pacific International Conference on Topology and Applications  2019.11 

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    Event date： 2019.11

    Language：English   Presentation type：Oral presentation (keynote)  

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  • Coarse compactifications and a generalization of Gromov products

    YAMAUCHI Takamitsu

    RIMS Symposium (Open) "Recent Developments in General Topology and its Related Fields"  2019.6 

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    Event date： 2019.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Gromov積の一般化について

    山内 貴光

    早稲田幾何学的トポロジーセミナー  2019.3 

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    Event date： 2019.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Coarse compactifications and controlled products Invited International conference

    YAMAUCHI Takamitsu

    Special Session on Recent Advances in Coarse Geometry, AMS Spring Southeastern Sectional Meeting  2019.3 

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    Event date： 2019.3

    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Dugundji空間とノルムの小さい線形拡張作用素の存在

    山内 貴光

    2018年度ジェネラルトポロジーシンポジウム  2018.12 

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    Event date： 2018.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Higson compactifications and Wallman-type compactifications

    YAMAUCHI Takamitsu

    RIMS meeting "Advances in General Topology and their Problems"  2018.6 

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    Event date： 2018.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Straight finite decomposition complexity and property A for coarse spaces Invited International conference

    YAMAUCHI Takamitsu

    The 2nd Pan Pacific International Conference on Topology and Applications  2017.11 

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    Event date： 2017.11

    Language：English   Presentation type：Oral presentation (invited, special)  

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  • Decomposition complexity and property A for coarse spaces

    YAMAUCHI Takamitsu

    RIMS Workshop "Research Trends on Set-theoretic and Geometric Topology and their cooperation with various branches"  2017.6 

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    Event date： 2017.6

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  • On infinite-dimensional properties for coarse spaces

    YAMAUCHI Takamitsu

    10th Waseda Geometric Topology Meeting  2017.3 

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    Event date： 2017.3

    Language：English   Presentation type：Oral presentation (general)  

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  • Higsonコロナの次元について

    山内 貴光

    2016年度つくばセミナー  2017.3 

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    Event date： 2017.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Hereditarily infinite-dimensional property for asymptotic dimension

    YAMAUCHI Takamitsu

    RIMS meeting "Set-Theoretic and Geometric Topology, and their applications"  2016.10 

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    Event date： 2016.10

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  • 内周が増大するグラフの列と漸近次元

    山内貴光

    第9回早稲田幾何学的トポロジー研究集会  2016.3 

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    Event date： 2016.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Hereditarily infinite-dimensional property for asymptotic dimension Invited International conference

    YAMAUCHI Takamitsu

    The 1st Pan Pacific International Conference on Topology and Applications  2015.11 

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    Event date： 2015.11

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  • 線型順序位相空間への写像に対する内挿定理

    山内貴光

    数理解析研究所研究集会「集合論的位相幾何学および幾何学的トポロジーの最近の動向と展望」  2015.11 

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    Event date： 2015.11

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Hereditarily infinite-dimensional spaces concerning asymptotic dimension Invited International conference

    YAMAUCHI Takamitsu

    Group actions and metric embeddings  2015.9 

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    Event date： 2015.9

    Language：English   Presentation type：Oral presentation (general)  

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  • C_0 coarse structures on uniform spaces Invited International conference

    YAMAUCHI Takamitsu

    International Conference on Set-Theoretic Topology and its Applications  2015.8 

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    Event date： 2015.8

    Language：English   Presentation type：Oral presentation (general)  

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  • 漸近次元とその無限次元性 Invited

    山内貴光

    第62回トポロジーシンポジウム  2015.8 

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    Event date： 2015.8

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Asymptotic property C of the countable sum of integers International conference

    YAMAUCHI Takamitsu

    Dubrovnik VIII - Geometric Topology, Geometric Group Theory & Dynamical Systems  2015.6 

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    Event date： 2015.6

    Language：English   Presentation type：Oral presentation (general)  

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  • Coarse幾何学における無限次元性について

    山内貴光

    第7回早稲田幾何学的トポロジー研究集会  2015.3 

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    Event date： 2015.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 漸近次元とその無限次元性について

    山内貴光

    幾何学的群論若手勉強会  2015.2 

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    Event date： 2015.2

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 漸近的性質Cについて

    山内貴光

    数理解析研究所研究集会「集合論的・幾何学的トポロジーと種々の分野の交流」  2014.10 

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    Event date： 2014.10

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On infinite dimensionality in coarse geometry Invited International conference

    YAMAUCHI Takamitsu

    International Workshop on Mathematical Sciences in Matsue  2014.10 

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    Event date： 2014.10

    Language：English   Presentation type：Oral presentation (general)  

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  • 整数群の可算直和の粗い幾何学における無限次元性について

    山内貴光

    日本数学会2014年度秋季総合分科会  2014.9 

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    Event date： 2014.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On factorizations of lower semicontinuous set-valued mappings

    山内貴光

    数理解析研究所研究集会「非線形解析学と凸解析学の研究」  2014.8 

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    Event date： 2014.8

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On factorizations of lower semicontinuous set-valued mappings

    山内貴光

    第49回位相空間論シンポジウム  2014.6 

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    Event date： 2014.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • C_0 coarse structures on uniforms spaces

    山内貴光

    数理解析研究所研究集会「集合論的及び幾何学的トポロジーの現状とその展望」  2013.10 

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    Event date： 2013.10

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On a simultaneous selection theorem International conference

    YAMAUCHI Takamitsu

    International Conference on Topology and Geometry 2013  2013.9 

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    Event date： 2013.9

    Language：English   Presentation type：Oral presentation (general)  

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  • Continuous selections for proximal continuous paraconvex-valued mappings International conference

    YAMAUCHI Takamitsu

    The eighth international conference on Nonlinear Analysis and Convex Analysis  2013.8 

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    Event date： 2013.8

    Language：English   Presentation type：Oral presentation (general)  

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  • On a simultaneous selection theorem

    山内貴光

    数理解析研究所研究集会「一般位相幾何学および幾何学的トポロジーの現状と諸問題」  2012.9 

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    Event date： 2012.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On continuous selections of paraconvex-valued mappings

    山内貴光

    第47回位相空間論シンポジウム  2012.6 

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    Event date： 2012.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 連続選択関数を与える線形作用素の存在について

    山内貴光

    つくばセミナー  2012.3 

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    Event date： 2012.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 連続選択関数の稠密な族の存在について

    山内貴光

    2011年度 General Topology シンポジウム  2011.12 

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    Event date： 2011.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Factorizations of upper semicontinuous compact-valued mappings

    山内貴光

    数理解析研究所研究集会「非線形解析学と凸解析学の研究」  2011.8 

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    Event date： 2011.8

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 上半連続集合値関数の分解について

    山内貴光

    第46回位相空間論シンポジウム  2011.6 

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    Event date： 2011.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 有限次元凸値関数に対する連続選択関数の存在

    山内貴光

    数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用」  2010.10 

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    Event date： 2010.10

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Continuous selections for set-valued mappings with finite-dimensional convex values International conference

    YAMAUCHI Takamitsu

    International Conference Japan-Mexico on Topology and its Applications  2010.9 

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    Event date： 2010.9 - 2010.10

    Language：English   Presentation type：Oral presentation (general)  

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  • Strong paracompactness and multi-selections

    山内貴光

    数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーに関する研究」  2009.10 

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    Event date： 2009.10

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On Cellina's approximate selection theorem

    山内貴光

    第44回位相空間論シンポジウム  2009.5 

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    Event date： 2009.5

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 連続選択関数の存在定理における集合値関数の閉値性について

    山内貴光

    つくばセミナー  2009.3 

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    Event date： 2009.3

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 支持集合を避けた連続選択関数の存在によって特徴付けられる位相的性質

    山内貴光

    日本数学会2008年度秋季総合分科会  2008.9 

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    Event date： 2008.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • An inverse of the Berge maximum theorem for infinite dimensional spaces International conference

    YAMAUCHI Takamitsu

    Asian Conference on Nonlinear Analysis and Optimization  2008.9 

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    Event date： 2008.9

    Language：English   Presentation type：Oral presentation (general)  

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  • Characterizations in terms of continuous selections avoiding supporting sets International conference

    YAMAUCHI Takamitsu

    Workshop on Continuous Selections and Hyperspaces  2007.12 

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    Event date： 2007.12

    Language：English   Presentation type：Oral presentation (general)  

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  • The role of countable paracompactness for continuous selections avoiding extreme points International conference

    YAMAUCHI Takamitsu

    International Conference on Topology and its Applications 2007  2007.12 

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    Event date： 2007.12

    Language：English   Presentation type：Oral presentation (general)  

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  • 端点を避けた連続選択写像の存在について

    山内貴光

    日本数学会2007年度秋季総合分科会  2007.9 

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    Event date： 2007.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On the existence of continuous selections avoiding extreme points

    山内貴光

    数理解析研究所研究集会「非線形解析学と凸解析学の研究」  2007.9 

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    Event date： 2007.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • On continuous selections avoiding extreme points

    山内貴光

    General Topology シンポジウム  2006.12 

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    Event date： 2006.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Continuous selections avoiding extreme points

    山内貴光

    数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーとその応用」  2006.10 

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    Event date： 2006.10

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 単体値写像の連続選択写像

    山内貴光

    日本数学会2006年度秋季総合分科会  2006.9 

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    Event date： 2006.9

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • A characterization of metrizable finitistic spaces and its applications to upper semicontinuous selections

    山内貴光

    General Topology シンポジウム  2005.12 

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    Event date： 2005.12

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Dieudonne completeness and continuous selections

    山内貴光

    第39回位相空間論シンポジウム  2004.5 

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    Event date： 2004.5

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • Dugundji spaces and linear extension operators of small norms

    YAMAUCHI Takamitsu

    Matsuyama Seminar on Topology, Geometry, Set Theory and their Applications  2018.11 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • Asymptotic dimension and graphs with large girth Invited

    山内 貴光

    松江セミナー  2017.12 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • 非コンパクト空間上の作用に対する同変漸近次元 Invited

    山内貴光

    東北大学大学院理学研究科数学専攻 談話会  2023.12 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • C_0 coarse structures on uniforms spaces

    山内貴光

    愛媛大学 数学談話会  2014.4 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 凸値関数に対する連続選択関数の存在問題について

    山内貴光

    松江セミナー  2008.3 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • Higson compactifications and their coronas Invited International conference

    YAMAUCHI Takamitsu

    Seminar at University of Sao Paulo  2017.8 

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Research Projects

  • Study on dimension for group actions and coarse geometry from a viewpoint of general topolgy

    2024.4 - 2029.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant amount：\4810000 （ Direct Cost: \3700000 、 Indirect Cost：\1110000 ）

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  • Study on dimension and topological spaces in coarse geometry

    2019.4 - 2024.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

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    Grant amount：\4160000 （ Direct Cost: \3200000 、 Indirect Cost：\960000 ）

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  • Study of dimension in coarse geometry and selections

    2014.4 - 2018.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)

    Yamauchi Takamitsu

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    Grant amount：\3900000 （ Direct Cost: \3000000 、 Indirect Cost：\900000 ）

    We mainly studied dimension in coarse geometry and the hyperspace selection problem in general topology. Concerning dimension in coarse geometry, we obtain results on infinite-dimensionality of the following two metric spaces: the countable direct sum of integers; a coarse disjoint union of graphs with large girth. We also have results on coarse structures, which are generalizations of metrics, and their infinite-dimensionality. Concerning the hyperspace selection problem, we obtain results on the existence of a continuous weak selection and orderability.

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  • Research on unified criteria in set-valued programming and its application

    2013.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    Kuroiwa Daishi, YAMAUCHI Takamitsu, MATSUSHITA Shin-ya, TANAKA Tamaki

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    Grant amount：\4940000 （ Direct Cost: \3800000 、 Indirect Cost：\1140000 ）

    Set-valued optimization problems are represented by using set-valued functions as objective and constraint functions in order to express various ideas in the real world. The study of set-valued optimization problems is required in the sense of theory and applications. However there are mainly two types of criteria of the solutions of the problem, l and u-types criteria, and also there is another s-type criterion.
    In this study, we give a unified framework for such various criteria including l, u, and s-types ones, and we observed the existence of solutions of the problems, generalized notions of convexity for set-valued maps, applications for vector-optimization problems with uncertainty, and so on.

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  • Computability, corse topology and the dimensions of metric spaces

    2010.4 - 2014.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    HATTORI Yasunao, KIMURA Makoto, YAMAUCHI Takamitsu, TSUIKI Hideki, YOKOI Katsuya, MATSUHASHI Eiichi, CHATYRKO Vitalij

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    Grant amount：\3900000 （ Direct Cost: \3000000 、 Indirect Cost：\900000 ）

    The main topics of the project are the following: (1) The applications of topological method to the theory of the computability and domain theory; and (2) the dimensions of metric spaces and its applications. (1) An early study on the Martin topology on the domain of the formal balls of a metric space suggested an importance of the Sorgenfrey-type topologies on the real line. We investigated several Sorgenfrey-type topologies, and we have a condition that a such topology is homeomorphic to the Sorgenfrey topology. We also have a test subspace of the Khalimski space for determining the n-dimensionality of its subspaces. (2) We obtained Hurewicz formulas for large inductive dimensions on normal spaces with additional conditins. We also have a result on the transfinite separation dimension of a subspace of the Hilbert cube, and investigated an approach which unifies several small inductive dimensions of spaces including the Menger-Uryshon dimension ind and the separation dimension t.

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  • Research on constraint qualification and solution method for set optimization programming

    2010 - 2012

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    KUROIWA Daishi, TANAKA Tamaki, YAMAUCHI Takamitsu, MATSUSHITA Shin-ya

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    Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）

    We study constraint qualification for optimization problems whose objective maps are set-valued maps based on criteria called `set optimization.’ We propose certain constraint qualifications for set optimization problems including a set optimization problem whose objective and constraint functions are set -valued convex functions. Also we study solution methods for well-posed set optimization problems.

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  • On the structure of computability on metric spaces, dimension and the complexities of descriptive set theory

    2007 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    HATTORI Yasunao, TSUIKI Hideki, YOKOI Katsuya, MAEDA Sadahiro, KIMURA Makoto, NOGURA Tsugunori, FURUMOCHI Tetsuo, YAMAUCHI Takamitsu

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    Grant amount：\3250000 （ Direct Cost: \2500000 、 Indirect Cost：\750000 ）

    We studied about the computability of metric spaces from the topological point of view. We also studied on set-theoretic topology and dimension theory of topological spaces. In particular, we studied the relations between the order and topological structures on the domains of the formal balls of metric spaces. Concerning dimension theory, we investigated the inductive dimension modulo absolute multiplicative class M(α) and additive class A(α), and constructed the examples which show the differences of the values of these dimensions. We also improved the additive theorem and the product theorem for the inductive dimensions. We also considered the spaces which are finite union of locally compact subspaces and gave a characterization of strong paracompactness by means of the selection of multi-valued mappings

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  • A notions of directional derivative for set-valued maps on set optimization programming and its applications

    2007 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    KUROIWA Daishi, TANAKA Tamaki, YAMAUCHI Takamitsu, MATSUSHITA Shin-ya

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    Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）

    We study optimization problems whose objective maps are set-valued maps based on criteria called 'set optimization.' We introduce a quotient space of a family of sets with an equivalence relation, we show the set optimization problems are embedded in the space, and we consider methodology to find solutions.

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Teaching Experience (On-campus)

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