• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2013 Fiscal Year Final Research Report

Computability, corse topology and the dimensions of metric spaces

Research Project

  • PDF
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
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
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.

  • Research Products

    (22 results)

All 2014 2013 2012 2011 2010

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (11 results) (of which Invited: 6 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 Pages: 21-25

    • DOI

      10.2298/FIL1401021C

    • Peer Reviewed
  • [Journal Article] On a simultaneous selection theorem2013

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Studia Mathematica

      Volume: Vol.215 Pages: 1-9

    • DOI

      10.4064/sm215-1-1

    • Peer Reviewed
  • [Journal Article] Small scattered topological invariants2013

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

      Matematychini Studii

      Volume: Vol.39 Pages: 212-222

    • 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

    • 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 Pages: 67-70

    • DOI

      10.4064/ba61-1-7

    • 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 Pages: 231-241

    • DOI

      10.1007/s10474-012-0207-6

    • 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

    • Peer Reviewed
  • [Journal Article] Factorizing usco mappings2012

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

      Topology and its Applications

      Volume: Vol.159 Pages: 2423-2433

    • DOI

      10.1016/j.topol.2011.11.061,10.1016/j.topol.2011.11.007

    • Peer Reviewed
  • [Journal Article] Around a Hurewicz's formula2012

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

      Topology and its Applications

      Volume: Vol.159 Pages: 1536-1544

    • DOI

      10.1016/j.topol.2010.12.017

    • 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 Pages: 1385-1393

    • DOI

      10.1002/mana.200910186

    • Peer Reviewed
  • [Journal Article] Strong paracompactness and multi-selections2010

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

      Topology and its Applications

      Volume: Vol.157 Pages: 1430-1438

    • DOI

      10.1016/j.topol.2009.06.017

    • Peer Reviewed
  • [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
    • Year and Date
      20130802-06
  • [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
  • [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
  • [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
    • 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
    • Invited
  • [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
    • Year and Date
      20110829-31
  • [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
    • 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
    • Year and Date
      20100626-30
    • 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
    • Year and Date
      20100617-19
    • Invited
  • [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
  • [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
    • Invited

URL: 

Published: 2015-07-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi