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

Classification of Higher dimensional Erdos spaces by singular selectors

Research Project

Project/Area Number 22540137
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionEhime University

Principal Investigator

NOGURA Tsugunori  愛媛大学, 名誉教授 (00036419)

Co-Investigator(Renkei-kenkyūsha) SHAKHMATOV Dmitri  愛媛大学, 理工学研究科, 教授 (90253294)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords順序数空間 / 連続弱選択関数 / 超空間 / 次元 / セレクター / 積空間 / 順序付け可能 / 順序付け可能性 / 順序 / 弱順序
Research Abstract

It is well known that topologies generated by continuous weak selections are weaker than the original topologies. We call a space is CWS if the topology is generated by continuous weak selections. We have established the fundamental properties of CWS spaces and calculate the CWS numbers of several examples. Also we investigate the weak orderability of product spaces. As applications we show that if the product of a GO-space and a first countable space is weakly orderable, then the GO-space must be hereditarily paracompact. Also we have shown that a pseudocompact space without isolated point is homeomorphic to the Cantor set if and only ifits cube X×X×X is weakly orderable.

Report

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

    (21 results)

All 2013 2012 2011 2010 Other

All Journal Article (15 results) (of which Peer Reviewed: 14 results) Presentation (6 results) (of which Invited: 1 results)

  • [Journal Article] Topologies generated by weak selection topologies2013

    • Author(s)
      Salvador Garcia-Ferreira
    • Journal Title

      Houston J. Math.

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Continuous weak selections for products2013

    • Author(s)
      Salvador Garcia-Ferreira
    • Journal Title

      Topology Appl.

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of kings in continuous tournaments2012

    • Author(s)
      Nagao, M.; Shakhmatov D.
    • Journal Title

      Topology Appl

      Volume: 159 Pages: 3089-3096

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quasi convexity dense and suitable sets in the arc component of a compact group2012

    • Author(s)
      Dikaranjan D.; Shakhmatov D.
    • Journal Title

      Math. Nachr

      Volume: 285 Pages: 476-485

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Kronecker-Weyl theorem fpr subsets of abelian groups2011

    • Author(s)
      Dikranjan D.;Shakhmatov D.
    • Journal Title

      Adv. Math.

      Volume: 226 Pages: 4776-4795

    • Related Report
      2012 Final Research Report
  • [Journal Article] Productivity of sequences with respect to a given weight function2011

    • Author(s)
      Dikranjan D.; Shakhmatov D.; Spevak J
    • Journal Title

      Topology Appl

      Volume: 158 Pages: 298-324

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak orderability of topological spaces2010

    • Author(s)
      Gutev V.; Nogura T
    • Journal Title

      Topology Appl

      Volume: 157 Pages: 1249-1274

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Set-maximal selections2010

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

      Topology Appl.

      Volume: 157 Pages: 53-61

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Markov-Zariski topology of abelian group2010

    • Author(s)
      Dikranjan D.; Shakhmatov, D
    • Journal Title

      J. Algebra

      Volume: 324 Pages: 1125-1158

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hewitt-Marczewski- Pondiczery type theorem for abelian groups and Markov's potential density2010

    • Author(s)
      Dikranjan D.; Shakhmatov D
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 138 Pages: 2979-2990

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Group valued continuous functions with the topology of pointwise convergence2010

    • Author(s)
      Shakhmatov D.; Spevak J
    • Journal Title

      Topology Appl

      Volume: 157 Pages: 1518-1540

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak orderability of topological spaces2010

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

      Topology and its Applications

      Volume: 157 Pages: 1249-1274

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Set-maximal selections2010

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

      Topology ans its Applications

      Volume: 157 Pages: 53-61

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topologies generated by weak selection topologies

    • Author(s)
      Garcia-Ferreira, S; Miyazaki, K; Nogura T.; Tomita, A. H.
    • Journal Title

      Houston J. Math.

      Volume: (accepted)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weakly orderability for products

    • Author(s)
      Garcia-Ferreira, S; Miyazaki, K; Nogura, T
    • Journal Title

      Topology Appl.

      Volume: (accepted)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Topologies generated by weak selection topologies2012

    • Author(s)
      Nogura T
    • Organizer
      International conference of Topology and related topics
    • Place of Presentation
      南京,(中国)
    • Related Report
      2012 Final Research Report
  • [Presentation] Graphtheoretic aspect of continuous weak selection2012

    • Author(s)
      Shakhmatov D
    • Organizer
      IVth Workshop on Coverings, Selections and Games in Topology
    • Place of Presentation
      Caserta(Italy)
    • Related Report
      2012 Final Research Report
  • [Presentation] Metrizability of compact groups via conditions on their dense subgroups2012

    • Author(s)
      Shakhmatov D
    • Organizer
      TOPOSYM 2011
    • Place of Presentation
      Prague(Czech Republic)
    • Related Report
      2012 Final Research Report
  • [Presentation] Topologies generated by weak selection topologies2012

    • Author(s)
      Tsugunori Nogura
    • Organizer
      International conference of topology and related topics
    • Place of Presentation
      南京大学(中国)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Two decades of pseudocompact group topologization problem2010

    • Author(s)
      Shakhmatov D
    • Place of Presentation
      Barcelona (Spain)
    • Related Report
      2012 Final Research Report
  • [Presentation] Topological properties of the Markov-Zariski topology of an abelian group2010

    • Author(s)
      Shakhmatov D
    • Organizer
      2010 International conference on Topology and its Applications
    • Place of Presentation
      Nafpaktos (Greece)
    • Related Report
      2012 Final Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi