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The set-theoretic study for the products with a monotonical normal factor in terms of stationary sets

Research Project

Project/Area Number 24540147
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKanagawa University

Principal Investigator

YAJIMA Yukinobu  神奈川大学, 工学部, 教授 (10142548)

Co-Investigator(Renkei-kenkyūsha) KEMOTO Nobuyuki  大分大学, 教育福祉科学部, 教授 (70161825)
HIRATA Yasushi  神奈川大学, 工学部, 特任准教授 (70375400)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsコンパクト空間 / 単調正規空間 / 積空間 / 定常集合 / 正規性 / 被覆性 / D-空間 / エレメンタリ―サブモデル / 正規 / △-パラコンパクト / △-正規 / 位相積空間
Outline of Final Research Achievements

The study of the products of monotonically normal spaces and various spaces were widely developed by Kemoto, Hirata and me. It was published as a long paper of 42 pages in 2014. The book titled "Recent Progress in General Topology III", which surveyed the investigations in this 10 years, was published in 2014. The survey titled "Covering properties" with Szeptycki was inserted in the book. Under the cooperation with Hirata, we have affirmatively solved some open problems for separation of diagonal in mootonically normal spaces. Moreover, we have proved the equivalence between normality and separation of diagonal for the products of a monotoncially normal space and a compact space.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (14 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (6 results) (of which Invited: 4 results) Book (3 results)

  • [Journal Article] The D-property of certain products2016

    • Author(s)
      Yasushi Hirata and Yukinobu Yajima
    • Journal Title

      Topology and its Applications

      Volume: -

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Separation of diagonal in monotonically normal spaces and their products2015

    • Author(s)
      Yasushi Hirata and Yukinobu Yajima
    • Journal Title

      Topology and its Applications

      Volume: -

    • Related Report
      2014 Annual Research Report 2013 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Products of monotonically normal spaces with various special factors2014

    • Author(s)
      Yasushi Hirata, Nobuyuki Kemoto and Yukinobu Yajima
    • Journal Title

      Topology and its Applications

      Volume: 164 Pages: 45-86

    • Related Report
      2014 Annual Research Report 2013 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The sup=max problem for the extent of generalized metric spaces2013

    • Author(s)
      Yasushi Hirata and Yukinobu Yajima
    • Journal Title

      Commentations Mathematicae Universitatis Carolinae

      Volume: 54 Pages: 245-257

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Products of monotonically normal spaces with factors defined by topological games2012

    • Author(s)
      Yukinobu Yajima
    • Journal Title

      Topology and its Applications

      Volume: 159 Pages: 1223-1235

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Separation of diagonal and the D-property in products2015

    • Author(s)
      Yukinobu Yajima
    • Organizer
      Symposium on General Topology
    • Place of Presentation
      南京大学(南京市,中国)
    • Year and Date
      2015-03-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the D-property of certain products2014

    • Author(s)
      平田康史,矢島幸信
    • Organizer
      RIMS研究集会「集合論的・幾何学的トポロジーと種々の分野の交流」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-10-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] 無限積空間におけるD-空間性2014

    • Author(s)
      平田康史,矢島幸信
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] Products of monotonically normal spaces with a compact space2012

    • Author(s)
      Yukinobu Yajima
    • Organizer
      International Conference on Topology and the related fields
    • Place of Presentation
      Nanjing Normal University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Products of monotonically normal spaces with various special factors2012

    • Author(s)
      Yukinobu Yajima
    • Organizer
      特になし (南京大学からの講演依頼)
    • Place of Presentation
      Nanjing University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Diagonal Separation in monotone normality and products

    • Author(s)
      Yukinobu Yajima
    • Organizer
      International Conference on Topology and Geometry 2013 (Joint with the 6th Japan- Mexico Topology Symposium)
    • Place of Presentation
      Shimane University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] "Covering properties" in Recent Progress in General Topology III2014

    • Author(s)
      P. Szeptycki and Yukinobu Yajima (edited by K.P.Hart, J van Mill and P. Simon)
    • Publisher
      Atlantis Press
    • Related Report
      2014 Annual Research Report
  • [Book] Recent Progress in General Topology III (edited by K.P. Hart, J. van Mill and P. Simon), 分担執筆の題名:Covering properties (pp. 801-824)2014

    • Author(s)
      Paul Szeptycki and Yukinobu Yajima
    • Total Pages
      903
    • Publisher
      Atlantis Press
    • Related Report
      2013 Research-status Report
  • [Book] Recent Progress in General Topology III (edited by J. van Mill, K.P. Hart and P. Simon), 分担執筆の題名:Covering properties2013

    • Author(s)
      Paul Szeptycki and Yukinobu Yajima
    • Publisher
      Springer
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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