From finite products to infinite products: investigations of topological properties of product spaces by means of set theoretical methods

• Project/Area Number: 19540141
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Oita University
• Principal Investigator: KEMOTO Nobuyuki Oita University, 教育福祉科学部, 教授 (70161825)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: topological spaces / finite products / infinite products / elementary submodels / hyperspaces / Hypersapce / orthocompact / countably metacompact / Sorgenfrey line / 位相空間 / 順序数 / 積空間 / 正規 / 次元 / 初等部分モデル / strong zero-dimensionality / elementary submodel / Vietoris topology / hyperspace / 線形順序付け可能 / β-sequence / compact closure / 可算パラコンパクト / 超空間 / rectangular

Research Abstract

Original purposes of this research were to investigate topological properties of infinite product spaces by means of these of finite product spaces. But by applying a set theoretical tool so called elementary submodels to product theory, we investigated toplogical properties of hyperspaces of all closed sets or all compact sets.

Research Products

• [Journal Article] Erratum to : "Normality and countable paracompactness of hyperspaces of ordinals", Topology and its Applications 154 (2007) 358-362 (2010)
  • Author(s): 家本宣幸
  • Journal Title: Top.Appl. 157 Pages: 2446-2447
  • Peer Reviewed
• [Journal Article] Strong zero-dimensionality of hyperspaces (2010)
  • Author(s): 家本宣幸, 寺澤順
  • Journal Title: Top.Appl. 157 Pages: 2376-2382
  • Peer Reviewed
• [Journal Article] Orderability of subspaces of well-orderable topological spaces (2010)
  • Author(s): 平田康史, 家本宣幸
  • Journal Title: Top.Appl. 157 Pages: 127-135
  • Peer Reviewed
• [Journal Article] Strong zero-dimensionality of hyperspaces (2010)
  • Author(s): 家本宣幸、寺澤順
  • Journal Title: Topology and its Applications Volume: 157 Pages: 2376-2382
  • Peer Reviewed
• [Journal Article] Erratum to : "Normality and countable paracompactness of hyperspaces of ordinals", Topology and its Applocations 154(2007)358-362 (2010)
  • Author(s): 家本宣幸
  • Journal Title: Topology and its Applications Volume: 157 Pages: 2446-2447
  • Peer Reviewed
• [Journal Article] Orderability of subspaces of well-orderable topological spaces (2010)
  • Author(s): Y. Hirata, N. Kemoto
  • Journal Title: Top.Appl. 157 Pages: 127-135
  • Peer Reviewed
• [Journal Article] Orderability of subspaces of well-orderable topological spaces (2010)
  • Author(s): 家本宣幸
  • Journal Title: Top.Appl. 157 Pages: 127-135
  • Peer Reviewed
• [Journal Article] Certain sequences with compact closure (2009)
  • Author(s): 家本宣幸, 矢島幸信
  • Journal Title: Top.Appl. 156 Pages: 1348-1354
  • Peer Reviewed
• [Journal Article] Certain sequences with compact closure (2009)
  • Author(s): N. Kemoto, Y. Yajima
  • Journal Title: Top.Appl. 156 Pages: 1348-1354
  • Peer Reviewed
• [Journal Article] Certain sequences with compact closure (2009)
  • Author(s): 家本 宣幸
  • Journal Title: Top. Appl. 156 Pages: 1348-1354
  • Peer Reviewed
• [Journal Article] Rectangular Products with ordinal factor (2007)
  • Author(s): 家本宣幸, 矢島幸信
  • Journal Title: Top.Appl. 154 Pages: 758-770
  • Peer Reviewed
• [Journal Article] Normality and countable paracompactness of hyperspaces of ordinals (2007)
  • Author(s): 家本宣幸
  • Journal Title: Top.Appl. 154 Pages: 358-362
  • Peer Reviewed
• [Journal Article] Rectangular Products with ordinal factors (2007)
  • Author(s): N. Kemoto, Y. Yajima
  • Journal Title: Top.Appl. 154 Pages: 758-770
  • Peer Reviewed
• [Journal Article] Normality and countable paracompactness of hyperspaces of ordinals (2007)
  • Author(s): N. Kemoto
  • Journal Title: Top.Appl. 154 Pages: 358-362
  • Peer Reviewed
• [Journal Article] Normality and countable paracompactness of hyperspaces of ordinals (2007)
  • Author(s): 家本 宣幸
  • Journal Title: Top. Appl. 154 Pages: 358-362
  • Peer Reviewed
• [Journal Article] Rectangular Products with ordinal factors (2007)
  • Author(s): 家本 宣幸、矢島 幸信
  • Journal Title: Top. Appl. 154 Pages: 758-770
  • Peer Reviewed
• [Presentation] Topological properties of hyperspaces : a set theoretical approach (2010)
  • Author(s): 家本宣幸
  • Organizer: International Conference Japan-Mexico on Topology and its Applications
  • Place of Presentation: Colima, Mexico
  • Year and Date: 2010-10-01
• [Presentation] Topological properties of hyperspaces : a set theoretical approach (2010)
  • Author(s): 家本宣幸
  • Organizer: International Conference Japan-Mexico on Topology and its Applications国際学会,招待講演
  • Place of Presentation: Colima, Mexico
• [Presentation] Applications of elementary submodels to hyperspaces (2009)
  • Author(s): 家本宣幸
  • Organizer: General Topology シンポジウム
  • Place of Presentation: 大分大学
  • Year and Date: 2009-12-17
• [Presentation] Applications of elementary submodels to hyperspaces (2009)
  • Author(s): 家本宣幸, 寺澤順
  • Organizer: 2009 General Topology シンポジウム
  • Place of Presentation: Oita Univ.
• [Presentation] Orderability of subspaces of well-orderable topological spaces (2008)
  • Author(s): 家本宣幸
  • Organizer: Advances in Set-Theoretic Topology国際学会・招待講演
  • Place of Presentation: Erice Sicily Italy
• [Presentation] Orderability of subspaces of well-orderable topological spaces (2008)
  • Author(s): N. Kemoto
  • Organizer: Advances in Set-Theoretic Topology
  • Place of Presentation: Erice Sicily Italy
• [Presentation] Applications of theory of stationary sets to topology (2007)
  • Author(s): 家本宣幸
  • Organizer: International Conference on Topology and its Applications 2007
  • Place of Presentation: Univ.Kyoto国際学会・招待講演
• [Presentation] The compact closure of sequences in monotonically normal spaces (2007)
  • Author(s): 家本宣幸, 矢島幸信
  • Organizer: 第43回位相空間論シンポジウム
  • Place of Presentation: 東京学芸大学
• [Presentation] Applications of theory of stationary sets to topology (2007)
  • Author(s): N. Kemoto
  • Organizer: International Conference on Topology and its Applications 2007
  • Place of Presentation: Univ. Kyoto
• [Presentation] Applications of theory of stationary sets to topology (2007)
  • Author(s): 家本 宣幸
  • Organizer: International Conference on Topology and its Applications 2007
  • Place of Presentation: 京都大学
• [Remarks]
  • URL: http://kitchom.ed.oita-u.ac.jp/~nkemoto/main.html
• [Remarks]
  • URL: http://kitchom.ed.oita-u.ac.jp/~nkemoto/main.html
• [Remarks]
  • URL: http://kitchom.ed.oita-u.ac.jp/~nkemoto/main.html