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Computability, corse topology and the dimensions of metric spaces

Research Project

Project/Area Number 22540084
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionShimane University

Principal Investigator

HATTORI Yasunao  島根大学, 総合理工学研究科(研究院), 教授 (20144553)

Co-Investigator(Kenkyū-buntansha) KIMURA Makoto  島根大学, 総合理工学部, 教授 (30186332)
YAMAUCHI Takamitsu  島根大学, 大学院総合理工学研究科, 講師 (00403444)
Co-Investigator(Renkei-kenkyūsha) TSUIKI Hideki  京都大学, 大学院人間環境学研究科, 教授 (10211377)
YOKOI Katsuya  東京慈恵会医科大学, 医学部, 教授 (90240184)
MATSUHASHI Eiichi  島根大学, 大学院総合理工学研究科, 講師 (60558518)
Research Collaborator CHATYRKO Vitalij  Linkoping University (Sweden), Associate Professor
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords距離空間 / ドメイン / 次元 / 分離次元 / Martin位相 / Sorgenfrey位相 / 形式的球体 / 小帰納次元 / 位相次元 / 計算可能性 / Khalimsky 空間 / Alexandroff 空間 / Sorgenfrey型位相 / 半順序構造 / 粗いトポロジー / 位相空間 / 超空間位相 / 半順序集合 / Scott位相 / コンパクト化 / 集合値関数 / 選択関数 / 被覆次元 / 帰納的次元
Research Abstract

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.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (50 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (21 results) (of which Peer Reviewed: 21 results) Presentation (29 results) (of which Invited: 8 results)

  • [Journal Article] Some remarks concerning semi-T_1/2 spaces2014

    • Author(s)
      Vitalij Chatyrko, Sang-Eon Han, Yasunao Hattori
    • Journal Title

      Filomat

      Volume: Vol.28 Issue: 1 Pages: 21-25

    • DOI

      10.2298/fil1401021c

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a simultaneous selection theorem2013

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Studia Mathematica

      Volume: Vol.215 Issue: 1 Pages: 1-9

    • DOI

      10.4064/sm215-1-1

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Small scattered topological invariants2013

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori
    • Journal Title

      Matematychini Studii

      Volume: Vol.39 Pages: 212-222

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A poset of topologies on the set of real numbers2013

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori
    • Journal Title

      Commentationes Mathematicae Universitatis Carolinae

      Volume: Vol.54 Pages: 189-196

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the separation dimension of Kω2013

    • Author(s)
      Yasunao Hattori, Jan van Mill
    • Journal Title

      Bull. Polish Acad. Sci.

      Volume: Vol.61 Issue: 1 Pages: 67-70

    • DOI

      10.4064/ba61-1-7

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A poset of topologies on the set of real numbers2013

    • Author(s)
      Vitalij Chatyrko and Yasunao Hattori
    • Journal Title

      Commentationes Mathematicae Universitatis Carolinae

      Volume: 54 Pages: 189-196

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Small scattered topological invariants2013

    • Author(s)
      Vitalij Chatyrko and Yasunao Hattori
    • Journal Title

      Matematychini Studii

      Volume: 39 Pages: 212-222

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the separation dimension of K_\omega2013

    • Author(s)
      Yasunao Hattori and Jan van Mill
    • Journal Title

      Bullten of the Polish Academy of Science, Mathematics

      Volume: 61 Pages: 67-70

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the classes of remainders of locally compact noncompact spaces2012

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori
    • Journal Title

      Acta Mathematica Hungarica

      Volume: Vol.137 Issue: 4 Pages: 231-241

    • DOI

      10.1007/s10474-012-0207-6

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Continuous selections for set-valued mappings with finite-dimensional convex values2012

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: Vol.159 Pages: 1219-1222

    • Related Report
      2013 Final Research Report 2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Factorizing usco mappings2012

    • Author(s)
      Valentin Gutev, Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: Vol.159 Issue: 4 Pages: 2423-2433

    • DOI

      10.1016/j.topol.2011.11.007

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Around a Hurewicz's formula2012

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori
    • Journal Title

      Topology and its Applications

      Volume: Vol.159 Issue: 6 Pages: 1536-1544

    • DOI

      10.1016/j.topol.2010.12.017

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Around a Hurewicz's formula2012

    • Author(s)
      Vitalij Chatyrko and Yasunao Hattori
    • Journal Title

      Topology and its Applications

      Volume: 159 Pages: 1536-1544

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the classes of remainders of locally compact noncompact spaces2012

    • Author(s)
      Vitalij Chatyrko and Yasunao Hattori
    • Journal Title

      Acta Mathematica Hungarica

      Volume: 137 Pages: 231-241

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Factorising usco mappings2012

    • Author(s)
      Valentin Gutev and Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 159 Pages: 2423-2433

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Factorising usco mappings2012

    • Author(s)
      V.Gutev, T.Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ricci solitons of compact real hypersurfaces in Kahler manifolds2011

    • Author(s)
      J.T. Cho, Makoto Kimura
    • Journal Title

      Math. Nachr.

      Volume: Vol.284 Issue: 11-12 Pages: 1385-1393

    • DOI

      10.1002/mana.200910186

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ricci slions of compact real hypersurfaces in Kahler manifolds2011

    • Author(s)
      J.T.Cho, M.Kimura
    • Journal Title

      Math.Nachr.

      Volume: 284 Pages: 1385-1393

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong paracompactness and multi-selections2010

    • Author(s)
      Valentin Gutev, Takamitsu Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: Vol.157 Issue: 8 Pages: 1430-1438

    • DOI

      10.1016/j.topol.2009.06.017

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strong paracompactness and multi-selections2010

    • Author(s)
      V.Gutev, T.Yamauchi
    • Journal Title

      Topology and its Applications

      Volume: 157 Pages: 1430-1438

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Around a Hurewicz's formula

    • Author(s)
      V.Chatyrko, Y.Hattori
    • Journal Title

      Topology and its Applications

      Volume: (To appear)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] On the separation dimension of Kω2013

    • Author(s)
      Yasunao Hattori, Jan van Mill(発表者:服部泰直)
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      Shimane University, Matsue, Japan
    • Year and Date
      2013-09-03
    • Related Report
      2013 Final Research Report
  • [Presentation] On a simultaneous selection theorem2013

    • Author(s)
      Valentin Gutev, Takamitsu Yamauchi(発表者:山内貴光)
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      Shimane University, Matsue, Japan
    • Year and Date
      2013-09-03
    • Related Report
      2013 Final Research Report
  • [Presentation] Continuous selections for proximal continuous paraconvex-valued mappings2013

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      International Conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Hirosaki University, Hirosaki, Aomori, Japan
    • Related Report
      2013 Final Research Report
  • [Presentation] On the separation dimension of K_{omega}2013

    • Author(s)
      Yasunao Hattori
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      島根大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Continuous selections for proximal continuous paraconvex-valued mappings2013

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      The Eighth International Conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      弘前大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] On a simultaneous selection theorem2013

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      島根大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] C_0 coarse structures on uniforms spaces2013

    • Author(s)
      山内貴光
    • Organizer
      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」
    • Place of Presentation
      京都大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Transfinite separation dimensions2012

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori(発表者:服部泰直)
    • Organizer
      International Conferece on Topology and the Related Fields
    • Place of Presentation
      Nanjin Normal University, Nanjin, China
    • Year and Date
      2012-09-23
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] Remainders of compactifications of spaces and locally compact spaces2012

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori(発表者:服部泰直)
    • Organizer
      2012 International Conference of the Honam Mathematical Society
    • Place of Presentation
      Jeju National University, Jeju, South Korea
    • Year and Date
      2012-06-15
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Remainders of compactifications of spaces and locally compact spaces2012

    • Author(s)
      Yasunao Hattori
    • Organizer
      2012 International Conference of the Honam Mathematical Society
    • Place of Presentation
      Jeju National University, Jeju, South Korea
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 可分局所コンパクト距離空間におけるコンパクト化の剰余空間2012

    • Author(s)
      服部泰直
    • Organizer
      第47回位相空間論シンポジウム
    • Place of Presentation
      愛媛大学(松山市)
    • Related Report
      2012 Annual Research Report
  • [Presentation] On continuous selections of paraconvex-valued mappings2012

    • Author(s)
      山内貴光
    • Organizer
      第47回位相空間論シンポジウム
    • Place of Presentation
      愛媛大学(松山市)
    • Related Report
      2012 Annual Research Report
  • [Presentation] On a simultaneous selection theorem2012

    • Author(s)
      山内貴光
    • Organizer
      京都大学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」
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 連続選択関数の稠密な族の存在について2011

    • Author(s)
      山内貴光
    • Organizer
      2011年度General Topology Symposium
    • Place of Presentation
      埼玉大学(埼玉県)
    • Year and Date
      2011-12-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] Factorizations of upper semicontinuous compact-valued mappings2011

    • Author(s)
      山内貴光
    • Organizer
      京都大学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」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2011-08-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Generalizations of Hurewicz's formula2011

    • Author(s)
      服部泰直
    • Organizer
      第46回位相空間論シンポジウム
    • Place of Presentation
      静岡大学(静岡県)
    • Year and Date
      2011-06-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] 上半連続集合値関数の分解について2011

    • Author(s)
      山内貴光
    • Organizer
      第46回位相空間論シンポジウム
    • Place of Presentation
      静岡大学(静岡県)
    • Year and Date
      2011-06-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Dimension lowering mapping theorems for inductive dimensions2011

    • Author(s)
      Yasunao Hattori
    • Organizer
      The Second International Workshop on Pure and Applied Topology
    • Place of Presentation
      Chonbuk National University, Jeonju, South Korea
    • Year and Date
      2011-04-29
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Dimension lowering mapping theorems for inductive dimensions2011

    • Author(s)
      Yasunao Hattori
    • Organizer
      The Second International Workshop on Pure and Applied Topology
    • Place of Presentation
      Chonbuk National University, Jeonju, South Korea(招待講演)
    • Year and Date
      2011-04-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Factorizations of upper semicontinuous compact-valued mappings2011

    • Author(s)
      山内貴光
    • Organizer
      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」
    • Place of Presentation
      京都大学
    • Related Report
      2013 Final Research Report
  • [Presentation] 有限次元凸値関数に対する連続選択関数の存在2010

    • Author(s)
      山内貴光
    • Organizer
      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」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] Continuous select ions for set-valued mappings with finite-dimensional convex values2010

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      International Conference Japan-Mexico on Topology and its Applications
    • Place of Presentation
      Universidad de Coli ma, Colima, Mexico
    • Year and Date
      2010-09-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Continuous selections for set-valued mappings with finite-dimensional convex values2010

    • Author(s)
      Takamitsu Yamauchi
    • Organizer
      International Conference Japan-Mexico on Topology and its Applications
    • Place of Presentation
      Universidad de Colima, Colima, Mexico
    • Year and Date
      2010-09-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] The remainders in extensions and finite unions of locally compact sets2010

    • Author(s)
      Yasunao Hattori
    • Organizer
      2010 International Conference on Topology and its Applications
    • Place of Presentation
      Technological Educational Institute of Messolonghi, Nafcaptos, Greece(招待講演)
    • Year and Date
      2010-06-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Special metrics which induce topological invariants2010

    • Author(s)
      Yasunao Hattori
    • Organizer
      2010 International Conference of the Honam Mathematical Society
    • Place of Presentation
      Mokpo National University Mokpo, South Korea(招待講演)
    • Year and Date
      2010-06-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Topological structures in the posets of formal balls on metric spaces2010

    • Author(s)
      Yasunao Hattori
    • Organizer
      Topology Workshop at Chonbuk National University
    • Place of Presentation
      Chonbuk National University, Jeonju, South Korea
    • Year and Date
      2010-06-16
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] The remainders in extensions and finite unions of locally compact sets2010

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori(発表者:服部泰直)
    • Organizer
      2010 International Conference on Topology and its Applications
    • Place of Presentation
      Nafcaptos, Greece
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Special metrics which induce topological invariants2010

    • Author(s)
      Yasunao Hattori
    • Organizer
      2010 International Conference of the Honam Mathematical Society
    • Place of Presentation
      Mokpo National University, Mopko, South Korea
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Compactifications and its remainders of spaces of finite unions of locally compact spaces

    • Author(s)
      Yasunao Hattori
    • Organizer
      Workshop on Topology
    • Place of Presentation
      Nanjin University, Nanjin, China
    • Related Report
      2012 Annual Research Report
    • Invited

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Published: 2010-08-23   Modified: 2019-07-29  

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