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Study of dimension in coarse geometry and selections

Research Project

Project/Area Number 26800040
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionEhime University

Principal Investigator

Yamauchi Takamitsu  愛媛大学, 理工学研究科(理学系), 准教授 (00403444)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordscoarse幾何 / 漸近次元 / 選択関数 / Coarse幾何学 / 次元 / 国際研究者交流 / メキシコ
Outline of Final Research Achievements

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.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (29 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (3 results) Journal Article (8 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 8 results,  Acknowledgement Compliant: 4 results) Presentation (18 results) (of which Int'l Joint Research: 5 results,  Invited: 8 results)

  • [Int'l Joint Research] Sao Paulo大学(ブラジル)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Nipissing大学(カナダ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Udine 大学(イタリア)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Another proof of a theorem of van Mill and Wattel on weak selections2018

    • Author(s)
      Koichi Motooka, Takamitsu Yamauchi
    • Journal Title

      Colloquium Mathematicum

      Volume: 印刷中 Issue: 2 Pages: 165-173

    • DOI

      10.4064/cm7214-9-2017

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On pseudocompact spaces with a weak selection2017

    • Author(s)
      Dikran Dikranjan, Kazumi Miyazaki, Tsugunori Nogura, Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 230 Pages: 490-505

    • DOI

      10.1016/j.topol.2017.08.019

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Straight finite decomposition complexity implies property A for coarse spaces2017

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 231 Pages: 329-336

    • DOI

      10.1016/j.topol.2017.09.034

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The existence of continuous weak selections and orderability-type properties in products and filter spaces2017

    • Author(s)
      K. Motooka, D. Shakhmatov, T. Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 232 Pages: 45-60

    • DOI

      10.1016/j.topol.2017.09.030

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Hereditarily infinite-dimensional property for asymptotic dimension and graphs with large girth2017

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Fundamenta Mathematicae

      Volume: 236 Issue: 2 Pages: 187-192

    • DOI

      10.4064/fm266-6-2016

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Insertion theorems for maps to linearly ordered topological spaces2015

    • Author(s)
      S. Garcia-Ferreira, Y.F. Ortiz-Castillo and T. Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 188 Pages: 74-81

    • DOI

      10.1016/j.topol.2015.03.011

    • NAID

      110010032933

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] C_0 coarse structures on uniform spaces2015

    • Author(s)
      Kotaro Mine, Atsushi Yamashita and Takamitsu Yamauchi
    • Journal Title

      Houston Journal of Mathematics

      Volume: 41 Pages: 1351-1358

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Asymptotic property C of the countable direct sum of the integers2015

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 184 Pages: 50-53

    • DOI

      10.1016/j.topol.2015.01.013

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] On infinite-dimensional properties for coarse spaces2017

    • Author(s)
      山内貴光
    • Organizer
      第10回早稲田幾何学的トポロジー研究集会
    • Place of Presentation
      早稲田大学 (東京都新宿区)
    • Year and Date
      2017-03-13
    • Related Report
      2016 Research-status Report
  • [Presentation] Higsonコロナの次元について2017

    • Author(s)
      山内貴光
    • Organizer
      2016年度つくばセミナー
    • Place of Presentation
      筑波大学 (茨城県つくば市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Research-status Report
  • [Presentation] 粗空間に対する分解複雑性と性質A2017

    • Author(s)
      山内貴光
    • Organizer
      RIMS 共同研究(公開型) 「集合論的・幾何学的トポロジーの動向と諸分野との連携」
    • Related Report
      2017 Annual Research Report
  • [Presentation] Higson compactifications and their coronas2017

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      Seminar at University of Sao Paulo
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Straight finite decomposition complexity and property A for coarse spaces2017

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      The 2nd Pan Pacific International Conference on Topology and Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic dimension and graphs with large girth2017

    • Author(s)
      山内貴光
    • Organizer
      松江セミナー
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 漸近次元に対する遺伝的無限次元性2016

    • Author(s)
      山内貴光
    • Organizer
      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その応用」
    • Place of Presentation
      京都大学 (京都府京都市)
    • Year and Date
      2016-10-17
    • Related Report
      2016 Research-status Report
  • [Presentation] 内周が増大するグラフの列と漸近次元2016

    • Author(s)
      山内貴光
    • Organizer
      第9回早稲田幾何学的トポロジー研究集会
    • Place of Presentation
      早稲田大学 (東京都新宿区)
    • Year and Date
      2016-03-14
    • Related Report
      2015 Research-status Report
  • [Presentation] Hereditarily infinite-dimensional property for asymptotic dimension2015

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      The 1st Pan Pacific International Conference on Topology and Applications
    • Place of Presentation
      Min Nan Normal University (Zhangzhou, China)
    • Year and Date
      2015-11-25
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 線型順序位相空間への写像に対する内挿定理2015

    • Author(s)
      山内貴光
    • Organizer
      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」
    • Place of Presentation
      京都大学 (京都府京都市)
    • Year and Date
      2015-11-16
    • Related Report
      2015 Research-status Report
  • [Presentation] Hereditarily infinite-dimensional spaces concerning asymptotic dimension2015

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      Group actions and metric embeddings
    • Place of Presentation
      京都大学 (京都府京都市)
    • Year and Date
      2015-09-08
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] C_0 coarse structures on uniform spaces2015

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      International Conference on Set-Theoretic Topology and its Applications
    • Place of Presentation
      神奈川大学 (神奈川県横浜市)
    • Year and Date
      2015-08-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 漸近次元とその無限次元性2015

    • Author(s)
      山内貴光
    • Organizer
      第62回トポロジーシンポジウム
    • Place of Presentation
      名古屋工業大学 (愛知県名古屋市)
    • Year and Date
      2015-08-06
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Asymptotic property C of the countable sum of integers2015

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      Dubrovnik VIII -- Geometric Topology, Geometric Group Theory & Dynamical Systems
    • Place of Presentation
      Inter-University Centre Dubrovnik (Dubrovnik, Croatia)
    • Year and Date
      2015-06-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Coarse幾何学における無限次元性について2015

    • Author(s)
      山内貴光
    • Organizer
      第7回早稲田幾何学的トポロジー研究集会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2015-03-25 – 2015-03-27
    • Related Report
      2014 Research-status Report
  • [Presentation] 漸近的性質Cについて2014

    • Author(s)
      山内貴光
    • Organizer
      京都大学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」
    • Place of Presentation
      京都大学
    • Year and Date
      2014-10-22 – 2014-10-24
    • Related Report
      2014 Research-status Report
  • [Presentation] On infinite dimensionality in coarse geometry2014

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      International Workshop on Mathematical Sciences in Matsue
    • Place of Presentation
      島根大学
    • Year and Date
      2014-10-11 – 2014-10-13
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 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2014

    • Author(s)
      山内貴光
    • Organizer
      日本数学会 2014年度秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2019-03-29  

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