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Construction of higher dimensional Erdos-type spaces with selectors and study of topological structure of hyperspaces

Research Project

Project/Area Number 19540134
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  Ehime University, 理工学研究科, 教授 (00036419)

Co-Investigator(Kenkyū-buntansha) SHAKHMATOV Dmitrii  愛媛大学, 理工学研究科, 教授 (90253294)
FUJITA Hiroshi  愛媛大学, 理工学研究科, 講師 (60238582)
HATTORI Yasunao  島根大学, 総合理工学部, 教授 (20144553)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords順序空間 / 連続選択関数 / 超空間 / 次元 / Vietoris位相 / (弱)連続選択関数 / (弱)順序づけ / 特異選択関数 / セレクター
Research Abstract

We have constructed an Erdos-type space whose inductive dimension is 2 and admits continuous selections. Also we have constructed a metrizable Erdos space whose covering dimension and small inductive dimension is n for any natural number n and admits a continuous weak selections. We have succeeded to characterize spaces by using set-maximal selections in the following cases : totally disconnected, 0 small inductive dimension and 0 large inductive dimension.

Report

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

    (38 results)

All 2010 2009 2008 2007 Other

All Journal Article (27 results) (of which Peer Reviewed: 27 results) Presentation (11 results)

  • [Journal Article] Weak orderability of topological spaces2010

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

      Topology Appl 157

      Pages: 1249-1274

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Set-maximal selections2010

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

      Topology Appl 157

      Pages: 53-61

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic topology of normed linear spaces2010

    • Author(s)
      Y. Hattori; H. Tsuiki
    • Journal Title

      Topology Appl 157

      Pages: 77-82

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Group-valued continuous functionswith the topology pointwise convergence2010

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

      Topology Appl

      Pages: 1518-1540

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quasi convex density and determining subgroups of compact abelian2010

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

      J. Math. Anal. Appl 363

      Pages: 42-48

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak orderability of topological spaces2010

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

      Topology and it's Applications (掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Set-maximal selections2010

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

      Topology and it's Applications 157

      Pages: 53-61

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak regularity and consecutive topologizations and regularizations of pretopologies2009

    • Author(s)
      S. Dolecki; H. Kunzi; T. Nogura
    • Journal Title

      Topology Appl 156

      Pages: 1306-1314

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Transfinite large inductive dimensions modulo absolute Borel classes2009

    • Author(s)
      V. Chatyrko; Y. Hattori
    • Journal Title

      J. Math. Soc. Japan 61

      Pages: 327-344

    • NAID

      10024905666

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minimal pseudocompact group topologies on free abelian groups2009

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

      Topology Appl 156

      Pages: 2039-2053

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Building suitable sets for locally compact groups by means of continuous selections2009

    • Author(s)
      D. Shakhmatov
    • Journal Title

      Topology Appl 156

      Pages: 1216-1223

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak regularity and consecutive topologizations and regularizations of pretopologies2009

    • Author(s)
      S.Dolecki, P.Kunzi, T.Nogura
    • Journal Title

      Topology and it's Applications 156

      Pages: 1306-1314

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak regularity and consective topologizations and regu larizations of pretopologies2009

    • Author(s)
      S. Dolecki, H. Kunzi & T. Nogura
    • Journal Title

      Topology and its Applications 156

      Pages: 1306-1314

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extensions of 2-point selections2008

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

      New Zealand J. Math 38

      Pages: 1-8

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak selections and flows in networks2008

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

      Comment. Math. Univ. Carolin 49

      Pages: 509-517

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Selections and totally disconnected spaces2008

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

      Topology Appl 155

      Pages: 824-829

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Addition and product theorems for ind2008

    • Author(s)
      V. Chatyrko; Y. Hattori
    • Journal Title

      Topology Appl 155

      Pages: 2202-2210

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lawson topology of the space of formal balls and hyperbolic topology2008

    • Author(s)
      H. Tsiki; Y. Hattori
    • Journal Title

      heoret. Comput. Sci 405

      Pages: 198-205

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinite dimensionality modulo absolute Borel classes2008

    • Author(s)
      V. Chatyrko; Y. Hattori
    • Journal Title

      Bull. Pol. Acad. Sci. Math 56

      Pages: 163-176

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reflection principle characterizing groups in which unconditionally closed sets are algebraic2008

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

      J. Group Theory 11

      Pages: 421-442

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Selections and totally disconnected spaces2008

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

      Topology and its Applications 155

      Pages: 509-517

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak selections and flows in network2008

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

      Comment. Math. Univ. Carolin 49

      Pages: 824-829

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence properties of hyperspaces2007

    • Author(s)
      G. Di Maio; Lj Kocinac; T. Nogura
    • Journal Title

      J. Korean Math. Soc 44

      Pages: 845-854

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] There is no upper bound of small transfinite compactness degree in metrizable spaces2007

    • Author(s)
      V. Chatyrko; Y. Hattori
    • Journal Title

      Topology Appl 154

      Pages: 1314-1320

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weight of closed subsets topologically generating a compact group2007

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

      Math. Nachr 280

      Pages: 505-522

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Convergence properties of hyperspaces2007

    • Author(s)
      G. di Maio, L.J. Kocinac, T. Nogura
    • Journal Title

      Journal of Korean Mathematical Society 44

      Pages: 845-854

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On dimensional properties of the generalized Smirnov's spaces

    • Author(s)
      V. Chatyrko; Y. Hattori
    • Journal Title

      Topology Appl 157

      Pages: 711-715

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] Remainders in extensions and finite unions of locally compact sets2009

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori (発表者:服部泰直)
    • Organizer
      京都大学数理解析研究所研究集会
    • Year and Date
      2009-10-15
    • Related Report
      2009 Final Research Report
  • [Presentation] Selections and Dimensions2009

    • Author(s)
      野倉嗣紀
    • Organizer
      第44回位相空間論シンポジウム
    • Place of Presentation
      島根大学
    • Year and Date
      2009-05-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] Selections and Dimensions2009

    • Author(s)
      Tsugunori Nogura
    • Organizer
      大44回位相空間論シンポジウム
    • Place of Presentation
      島根大学
    • Year and Date
      2009-05-23
    • Related Report
      2009 Final Research Report
  • [Presentation] Borel classes di mension and generalization of Smirn ov's compacta2008

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori, (発表者:服部泰直)
    • Organizer
      京都大学数理解析研究所研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2008-10-08
    • Related Report
      2009 Final Research Report
  • [Presentation] Lawson topology o f the space of formal balls and the hyperbolic topology of a metric space2008

    • Author(s)
      Yasunao Hattori, Hideki Tsuiki, (発表者:服部泰直)
    • Organizer
      The 23th Summer Conference on To pology and its Applications
    • Place of Presentation
      Universi ty of National Autonomous of Mexic o, Mexico City
    • Year and Date
      2008-07-30
    • Related Report
      2009 Final Research Report
  • [Presentation] Dimensional prop erties of the generalized Smirnov's s paces, Advanced in Set-Theoretic To pology2008

    • Author(s)
      Vitalij Chatyrko, Yasunao Hattori, (発表者:服部泰直)
    • Organizer
      International Center for Scien tificCulture "E. Majorana", School of Mathematics
    • Place of Presentation
      Erice, Italy
    • Year and Date
      2008-06-12
    • Related Report
      2009 Final Research Report
  • [Presentation] Continuous selections and Dimensions2008

    • Author(s)
      Tsugunori Nogura
    • Organizer
      Advances in Set-Theoretic Topology
    • Place of Presentation
      Erice, Italy(招待講演)
    • Year and Date
      2008-06-09
    • Related Report
      2009 Final Research Report
  • [Presentation] Selections and Dimensions2008

    • Author(s)
      野倉 嗣紀
    • Organizer
      Advances in Set-theoretic topology
    • Place of Presentation
      Erice (イタリア)
    • Year and Date
      2008-06-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] The hyperbolic topolo gy of normed linear spaces2007

    • Author(s)
      Yasunao Hattori, Hideki Tsuiki, (発表者:服部泰直)
    • Organizer
      Internat ional Conferences in Topology and it s Applications 2007 at Kyoto, Jointly with 4th Japan-Mexico Topolog Conf erence
    • Place of Presentation
      京都大学
    • Year and Date
      2007-12-05
    • Related Report
      2009 Final Research Report
  • [Presentation] Selections and Di mensions2007

    • Author(s)
      Tsugunori Nogura
    • Organizer
      22 Summer Conference on Topology and its Applications
    • Place of Presentation
      Castellon, Spain
    • Year and Date
      2007-07-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Selections and Dimensions2007

    • Author(s)
      野倉 嗣紀
    • Organizer
      22 Summer Conference on Topology and its Appli cations
    • Place of Presentation
      Castellion(Spain)
    • Year and Date
      2007-07-24
    • Related Report
      2007 Annual Research Report

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

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