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Set-theoretic approach to the extension problem of continuous functions on topological spaces

Research Project

Project/Area Number 19540122
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 InstitutionShizuoka University

Principal Investigator

OHTA Haruto  Shizuoka University, 教育学部, 教授 (40126769)

Co-Investigator(Kenkyū-buntansha) YAMADA Kohzo  静岡大学, 教育学部, 教授 (00200717)
TAMANO Kenichi  横浜国立大学, 大学院・工学研究院, 教授 (90171892)
YAMAZAKI Kaori  高崎経済大学, 経済学部, 准教授 (80301076)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords数学基礎論 / 位相空間 / 集合論 / 連続関数 / 拡張問題 / 連続関数の拡張 / Dowker空間 / 正規空間 / 実コンパクト / 関数列の収束 / 完全正規空間 / Scheepers予想 / QN空間 / wQN空間 / 至るところ第1類 / 可測濃度 / 拡張 / 距離空間 / 独立部分基底
Research Abstract

本研究は,トポロジーのキー・ワードの1つである連続写像の拡張に関する研究である。特に,位相空間上の連続関数の拡張問題を集合論を応用することによって研究する。位相空間の任意の閉集合の可算局所有限開被覆が全体空間の可算局所有限開被覆に拡張可能であるためには,任意のσ-局所コンパクト距離空間との直積が矩形正規であることが必要十分であることを証明して,T.C.Przymusinskiによって1983年に提起された問題を肯定的に解決した。

Report

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

    (17 results)

All 2009 2007 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (4 results) Book (2 results) Remarks (3 results)

  • [Journal Article] Sequences of semi-continuous functions accompanying continuous functions2009

    • Author(s)
      Haruto Ohta, Masami Sakai
    • Journal Title

      Topology and its Applications Vol.156

      Pages: 2683-2691

    • NAID

      120001662293

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Przymusinski's characterization of countably Katetov spaces2009

    • Author(s)
      Haruto Ohta
    • Journal Title

      Topology Proceedings Vol.34

      Pages: 147-159

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rectangular normality of product spaces2009

    • Author(s)
      Haruto Ohta
    • Journal Title

      Questions and Answers in General Topology Vol.27

      Pages: 23-29

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Przymusinski's characterization of countably Katetov spaces2009

    • Author(s)
      Haruto Ohta
    • Journal Title

      Topology Proceedings 34

      Pages: 147-159

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

    • Author(s)
      Haruto Ohta, Masami Sakai
    • Journal Title

      Topology and its Applications 156

      Pages: 2683-2691

    • NAID

      120001662293

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rectangular normality of product spaces2009

    • Author(s)
      Haruto Ohta
    • Journal Title

      Queat ions and Answers in General Topology 27

      Pages: 23-29

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Locally bounded setvalued mappings and monotone countable paracompactness2007

    • Author(s)
      Kaori Yamazaki
    • Journal Title

      Topology and its Applications Vol.154

      Pages: 2817-2825

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Locally bounded set-valued mappings and monotone countable paracompactness2007

    • Author(s)
      Kaori Yamazaki
    • Journal Title

      Topology and its Applications 154

      Pages: 2817-2825

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Sequences of semicontinuous functions accompanying continuous functions2009

    • Author(s)
      大田春外
    • Organizer
      日本数学会2009年度秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Sequences of semicontinuous functions accompanying continuous functions2009

    • Author(s)
      大田春外
    • Organizer
      2009日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 自己稠密可分距離空間の独立部分基底2009

    • Author(s)
      大田春外
    • Organizer
      日本数学会2007年度秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2009-09-23
    • Related Report
      2009 Final Research Report
  • [Presentation] 自己稠密可分距離空間の独立部分基底2007

    • Author(s)
      大田 春外
    • Organizer
      日本数学会2007年度秋期総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Book] Extension problems of realvalued continuous functions2007

    • Author(s)
      Haruto Ohta, Kaori Yamazaki
    • Publisher
      Elsevier
    • Related Report
      2009 Final Research Report
  • [Book] E.Pearl(ed.)Open Problems in Topology II, Extension problems of real-valued continuous functions(pp.35-45)2007

    • Author(s)
      Haruto Ohta
    • Total Pages
      763
    • Publisher
      Elsevier
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www.ipc.shizuoka.ac.jp/~echohta/welcome.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.ipc.shizuoka.ac.jp/~echohta/top.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.ipc.shizuoka.ac.jp/~echohta/jpage01.html

    • Related Report
      2008 Annual Research Report

URL: 

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

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