Updated on 2025/04/04

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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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

    Web of Science

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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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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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Teaching Experience (On-campus)

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