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A study on special subsets of real numbers derived from local properties of function spaces and their critical cardinalities

Research Project

Project/Area Number 19540151
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 InstitutionKanagawa University

Principal Investigator

SAKAI Masami  Kanagawa University, 工学部, 教授 (60215598)

Co-Investigator(Kenkyū-buntansha) YAJIMA Yukinobu  神奈川大学, 工学部, 教授 (10142548)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2008: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2007: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Keywords数学基礎論 / 関数空間 / 特異部分集合 / 臨界濃度
Research Abstract

For a topological space X, we denote by Cp(X) the space of all continuous functions with the topology of pointwise convergence. It is known that a local property of Cp(X) can be characterized in terms of a covering property of X. For example, Gerlits and Nagy showed that Cp(X) is Frechet if and only if X is a γ-set. A γ-set is strong measure zero, so some local properties of Cp(X) are related with some singular sets of reals appeared in descriptive set-theory. We studied some relations between local properties of Cp(X) and singular sets X of reals, and answered some open problems posed by Scheepers, Bukovsky and so on.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (30 results)

All 2010 2009 2008 2007 Other

All Journal Article (20 results) (of which Peer Reviewed: 20 results) Presentation (10 results)

  • [Journal Article] conjecture onσ-CF* pseudo-bases2010

    • Author(s)
      M. Sakai, Mizokami, Lin's
    • Journal Title

      Topology Appl. 157

      Pages: 152-156

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Selection principles and upper semicontinuous functions2009

    • Author(s)
      M. Sakai
    • Journal Title

      Colloquium Math 117

      Pages: 251-256

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sequences of semicontinuous functions accompanying continuous functions2009

    • Author(s)
      M. Sakai, H. Ohta
    • Journal Title

      Topology Appl. 156

      Pages: 2683-2691

    • NAID

      120001662293

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Menger subsets of the Sorgenfrey line2009

    • Author(s)
      M. Sakai
    • Journal Title

      Proc. Amer. Math. Soc. 137

      Pages: 3129-3138

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Menger subsets of the Sorgenfrey line2009

    • Author(s)
      酒井政美
    • Journal Title

      Proceedings Amer.Math.Soc. 137

      Pages: 3129-3138

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sequences of semicontinuous functions accompanying continuous functions2009

    • Author(s)
      酒井政美・大田春外
    • Journal Title

      Topology and its Applications 156

      Pages: 2683-2691

    • NAID

      120001662293

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Selection principles and upper semicontinuous functions2009

    • Author(s)
      酒井政美
    • Journal Title

      Colloquium Mathematicum 117

      Pages: 251-256

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Function spaces with a countable cs*-network at a point2008

    • Author(s)
      M. Sakai
    • Journal Title

      Topology Appl. 156

      Pages: 117-123

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mapping theorems onχ-spaces2008

    • Author(s)
      M. Sakai
    • Journal Title

      Comm. Math. Univ. Calolinae 49

      Pages: 163-167

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mapping theorems on Aleph-spaces2008

    • Author(s)
      酒井 政美
    • Journal Title

      Comment at iones Math. Univ. Carolinae 49

      Pages: 163-167

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Function spaces with a countable cs*-ne twork at a point2008

    • Author(s)
      酒井 政美
    • Journal Title

      Topology and its Applications 156

      Pages: 117-123

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] k-Frechet Urysohn property of Ck (X)2007

    • Author(s)
      M. Sakai
    • Journal Title

      Topology Appl. 154

      Pages: 516-1520

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The sequence selection properties of Cp (X)2007

    • Author(s)
      M. Sakai
    • Journal Title

      Topology Appl. 154

      Pages: 552-560

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak-open maps and sequence-covering maps2007

    • Author(s)
      M. Sakai
    • Journal Title

      Sci. Math. Japonicae 66

      Pages: 67-71

    • NAID

      10019758561

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The sequence selection properties of Cp(X)2007

    • Author(s)
      酒井 政美
    • Journal Title

      Topology and its Applications 154

      Pages: 552-560

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] k-Frechet Urysohn property of Ck(X)2007

    • Author(s)
      酒井 政美
    • Journal Title

      Topology and its Applications 154

      Pages: 1516-1520

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On dense subspaces of Cp(X)2007

    • Author(s)
      酒井 政美
    • Journal Title

      Note di Matematica 27

      Pages: 41-46

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak open maps and sequence-covering maps2007

    • Author(s)
      酒井 政美
    • Journal Title

      Scientiae Mathematicae Japonicae 66

      Pages: 67-71

    • NAID

      10019758561

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Counterexamples on the images of locally separable metric spaces2007

    • Author(s)
      酒井 政美, Shou Lin
    • Journal Title

      Topology Proceedings 31

      Pages: 181-187

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Ramsey property for Cp (X)

    • Author(s)
      M. Sakai
    • Journal Title

      to appear in Acta Math. Hungur.

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] The Ramsey property for Cp (X)2009

    • Author(s)
      酒井政美
    • Organizer
      一般位相幾何及び幾何学的トポロジーに関する研究
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2009 Final Research Report
  • [Presentation] Menger subsets of the Sorgenfrey line2009

    • Author(s)
      酒井政美
    • Organizer
      24th Summer Conference on Topology and its Applications
    • Place of Presentation
      Brno, Czech Republic
    • Related Report
      2009 Final Research Report
  • [Presentation] Menger subsets of the Sorgenfrey line2009

    • Author(s)
      酒井政美
    • Organizer
      24_<th> Summer Conference on Topology and its Applications
    • Place of Presentation
      Brno, Czech Republic
    • Related Report
      2009 Annual Research Report
  • [Presentation] Totally paracompact spaces and remaining problems2008

    • Author(s)
      酒井政美
    • Organizer
      General Topology Symposium
    • Place of Presentation
      高崎経済大学
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Mizokami and Lin's conjecture, Advances in Set-theoretic Topology2008

    • Author(s)
      酒井政美
    • Organizer
      International Centre for Scientific Culture "E. Majorana" School of Mathematics "G. Stampacchia
    • Place of Presentation
      Italy
    • Related Report
      2009 Final Research Report
  • [Presentation] Mizokami and Lin's conjecture2008

    • Author(s)
      酒井 政美
    • Organizer
      Advances in Set-theoretic Topology
    • Place of Presentation
      Internat ional Centre for Scient ific Culture, イタリア
    • Related Report
      2008 Annual Research Report
  • [Presentation] Function spaces with a countable cs*-network at a point2007

    • Author(s)
      酒井政美
    • Organizer
      International Conference on Topology and its Applications 2007 at Kyoto
    • Place of Presentation
      京都大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Around the strong Pytkeev property of function spaces2007

    • Author(s)
      酒井政美
    • Organizer
      III Workshop on Coverings, Selections and Games in Topology
    • Place of Presentation
      Vrnjacka Banja, Serbia.
    • Related Report
      2009 Final Research Report
  • [Presentation] Around the strong Pytkeev property of function spaces2007

    • Author(s)
      酒井 政美
    • Organizer
      III Workshop on Coverings, Selections and Games in Topology
    • Place of Presentation
      Vrnjacka Banja, Serbia
    • Related Report
      2007 Annual Research Report
  • [Presentation] Function spaces with a countable cs^*-network at a point2007

    • Author(s)
      酒井 政美
    • Organizer
      International Conference on Topology and its Applications 2007 at Kyoto
    • Place of Presentation
      京都大学
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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