Graduate School of Science and Engineering（Science）
理工学専攻（数理科学）
日本語
Update date：2025/01/08
Professor
Yamauchi Takamitsu

Research History

  1. 2005/04-2008/03Interdisciplinary Faculty of Science and Engineering, Shimane UniversityTeaching Associate
  2. 2008/04-2009/03Department of General Education, Kure National College of TechnologyLecturer
  3. 2009/04-2012/03Interdisciplinary Faculty of Science and Engineering, Shimane UniversityLecturer
  4. 2012/04-2014/03Interdisciplinary Graduate School of Science and Engineering, Shimane UniversityLecturer
  5. 2014/04-2020/09Graduate School of Science and Engineering, Ehime UniversityAssociate Professor
  6. 2020/10-presentGraduate School of Science and Engineering, Ehime UniversityProfessor

Education

  1. University of Tsukuba1997/042001/03
  2. University of Tsukuba2001/042006/03

Degree

  1. Master of ScienceUniversity of Tsukuba2003/03
  2. Doctor of ScienceUniversity of Tsukuba2006/03

Research Areas

Research Interests

  1. continuous selection
  2. set-valued mapping
  3. topological space
  4. metirc space
  5. dimension theory
  6. general topology

Research Projects

  1. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Study on dimension and topological spaces in coarse geometryGrant-in-Aid for Scientific Research (C)2019/04-2024/03
  2. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)Study of dimension in coarse geometry and selectionsGrant-in-Aid for Young Scientists (B)2014/04-2018/03We 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.
  3. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Research on unified criteria in set-valued programming and its applicationGrant-in-Aid for Scientific Research (C)2013/04-2016/03Set-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.
  4. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Computability, corse topology and the dimensions of metric spacesGrant-in-Aid for Scientific Research (C)2010/04-2014/03The 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.
  5. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)Research on constraint qualification and solution method for set optimization programmingGrant-in-Aid for Scientific Research (C)2010-2012We 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.
View details...

Papers

  1. Coarse compactifications and controlled products2022/12Tomohiro Fukaya Shin-ichi Oguni Takamitsu YamauchiJournal of Topology and Analysis14/ 04, 875-900Research paper (scientific journal)10.1142/s1793525321500102URLWorld Scientific Pub Co Pte LtdWe 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.
  2. Coarse infinite-dimensionality of hyperspaces of finite subsets2022/03Thomas Weighill Takamitsu Yamauchi Nicolò ZavaEuropean Journal of Mathematics8/ 1, 335-355Research paper (scientific journal)10.1007/s40879-021-00515-3We 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.
  3. On transfinite asymptotic dimension (Research Trends on General Topology and its Related Fields)2022/01Yamauchi TakamitsuRIMS Kokyuroku2209(MISC) Introduction and explanation (bulletin of university, research institution)京都大学数理解析研究所
  4. Connectedness properties of the Higson corona of the half line2021/09/01Takamitsu YamauchiTopology and its Applications301, 107542-26ppResearch paper (scientific journal)10.1016/j.topol.2020.107542Elsevier BVIt 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.
  5. Transfinite asymptotic dimension and APD profiles2021/05/15Takamitsu YamauchiTopology and its Applications295, 107675-7ppResearch paper (scientific journal)10.1016/j.topol.2021.107675Elsevier BVWe 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.
View details...

Presentations

  1. On a characterization of equivariant asymptotic dimension2024 早稲田幾何学的トポロジー研究集会2024/03/06Oral presentation(general)
  2. 非コンパクト空間上の作用に対する同変漸近次元東北大学大学院理学研究科数学専攻 談話会2023/12/11Public discourse, seminar, tutorial, course, lecture and others
  3. On dynamic asymptotic dimension of Stone-Čech extensions of proper cocomopact actions2023年度ジェネラルトポロジーシンポジウム2023/12/06Oral presentation(general)
  4. Group coarse structures on locally compact abelian groupsMini-symposium ``Topology and Applications'' in Mathematics Days in Sofia2023/07/12Oral presentation(invited, special)
  5. Group coarse structures on locally compact abelian groupsGeneral Topology Symposium 20222022/12/07Oral presentation(general)
View details...

Allotted Class

  1. 2024Basic Mathematics
  2. 2024Basic Mathematics
  3. 2024Advanced Geometry
  4. 2024Set Theory and TopologyⅡ
  5. 2024Introduction to Analysis
View details...

Professional Memberships

  1. 2005/04-presentThe Mathematical Society of Japan
View details...