New development in topology with the method of set theory

• Project/Area Number: 21740080
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka Prefecture University
• Principal Investigator: KADA Masaru 大阪府立大学, 理学系研究科, 准教授 (00312447)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 位相空間論 / 強制法 / 巨大基数公理 / 距離化可能空間 / コンパクト化 / リンデレーフ空間 / 無限ゲーム / 数学基礎論 / Galois-Tukey connection / 可測基数

Research Abstract

The subjects of this project include:
(1) Investigation into order structures consisting of sets of compatible metrics on metrizable spaces;
(2) Interplay between preservation of the Lindelof property under forcing extension and infinite games on Boolean algebras;
(3) The role of large cardinal axioms in bounding the cardinality of Lindelof spaces whose points are Gδ;
(4) Preservation of convergence of a sequence to a set under forcing extensions. Most of achievements in this project were obtained using not only traditional method in general topology but also set-theoretic method such as forcing.

Research Products

• [Journal Article] Galois-Tukey connection involving sets of metrics. (2012)
  • Author(s): Masaru Kada and Yasuo Yoshinobu
  • Journal Title: Tsukuba J. Math Volume: Vol. 36 Pages: 53-66
  • NAID: 120006349361
  • Peer Reviewed
• [Journal Article] Galois-Tukey connection involving sets of metrics (2012)
  • Author(s): Masaru Kada and Yasuo Yoshinobu
  • Journal Title: Tsukuba Journal of Mathematics Volume: 36 Pages: 53-66
  • NAID: 120006349361
  • Peer Reviewed
• [Journal Article] Galois-Tukey connection involving sets of metrics (2012)
  • Author(s): Masaru Kada, Yasuo Yoshinobu
  • Journal Title: Tsukuba Journal of Mathematics Volume: Vol.36(印刷中につき未確定)
  • NAID: 120006349361
  • Peer Reviewed
• [Journal Article] reserving the Lindelof property under forcing extensions. (2011)
  • Author(s): Masaru Kada
  • Journal Title: Topology Proceedings Volume: Vol. 38 Pages: 237-251
  • Peer Reviewed
• [Journal Article] コーエン強制, ランダム強制に関する位相空間の性質の保存 (2011)
  • Author(s): 嘉田勝
  • Journal Title: 数理解析研究所講究録 1728「一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用」 Pages: 72-78
• [Journal Article] Remarks on Scheepers' theorem on the cardinality of Lindelof spaces. (2011)
  • Author(s): 嘉田勝
  • Journal Title: 数理解析研究所講究録 1754「大きな無限と小さな無限の相互関係」 Pages: 75-80
• [Journal Article] Preserving the Lindelof property under forcing extensions (2011)
  • Author(s): Masaru Kada
  • Journal Title: Topology Proceedings Volume: Vol.38 Pages: 237-251
  • Peer Reviewed
• [Journal Article] コーエン強制,ランダム強制に関する位相空間の性質の保存 (2011)
  • Author(s): 嘉田勝
  • Journal Title: 数理解析研究所講究録 Volume: 1728 Pages: 72-78
• [Journal Article] How many miles to βX? II - Approximations to βX versus cofinal types of sets of metrics. (2010)
  • Author(s): Masaru Kada
  • Journal Title: Topology and its Applications Volume: Vol.157 Pages: 1460-1464
  • NAID: 120006719693
  • Peer Reviewed
• [Journal Article] Remarks on the preservation of topological covering properties under Cohen forcing (2010)
  • Author(s): 嘉田勝
  • Journal Title: 数理解析研究所講究録 1686「無限集合上の組合せ論と強制法理論」 Pages: 63-72
• [Journal Article] How many miles to β X?II-Approximations to β X versus cofinal types of sets of metrics (2010)
  • Author(s): Masaru Kada
  • Journal Title: Topology and its Applications Volume: Vol.157 Pages: 1460-1464
  • NAID: 120006719693
  • Peer Reviewed
• [Journal Article] Remarks on Scheepers' theorem on the cardinality of Lindelof spaces
  • Author(s): 嘉田勝
  • Journal Title: 数理解析研究所講究録 Volume: (印刷中)
• [Journal Article] Remarks on the preservation of topological covering properties under Cohen forcing
  • Author(s): Masaru Kada
  • Journal Title: 数理解析研究所講究録 (印刷中)
• [Presentation] 点列の集合への収束と強制拡大 (2012)
  • Author(s): 岩佐明,嘉田勝,加茂静夫
  • Organizer: 2012年度General Topology Symposium.
  • Place of Presentation: 神戸大学
  • Year and Date: 2012-12-13
• [Presentation] A technique for proving preservation of topological properties under forcing extensions (2012)
  • Author(s): 嘉田勝
  • Organizer: 強制法による拡大と巨大基数(RIMS 研究集会)
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-12-06
• [Presentation] 距離関数の順序構造とGalois-Tukey connection. (2012)
  • Author(s): 嘉田勝
  • Organizer: 日本数学会秋季総合分科会 トポロジー分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-21
• [Presentation] バビロンまでは何マイル? -コンパクト化の近似と集合論 (2012)
  • Author(s): 嘉田勝
  • Organizer: 第59回トポロジーシンポジウム(招待講演)
  • Place of Presentation: 佐賀大学
  • Year and Date: 2012-08-13
• [Presentation] 強制法による位相的性質の保存と無限ゲーム (2012)
  • Author(s): 嘉田勝
  • Organizer: 日本数学会年会 数学基礎論および歴史分科会.
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-27
• [Presentation] 強制法による位相的性質の保存と無限ゲーム (2012)
  • Author(s): 嘉田勝
  • Organizer: 日本数学会年会数学基礎論および歴史分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-27
• [Presentation] Remarks on Scheepers' theorem on the cardinality of Lindelof spaces. (2012)
  • Author(s): Masaru Kada.
  • Organizer: Joint FWF-JSPS Seminar on Forcing in Set Theory
  • Place of Presentation: 神戸大学
  • Year and Date: 2012-01-25
• [Presentation] Remarks on Scheepers' theorem on the cardinality of Lindelof spaces (2012)
  • Author(s): Masaru Kada
  • Organizer: Joint FWF-JSPS Seminar on Forcing in Set Theory
  • Place of Presentation: 神戸大学
  • Year and Date: 2012-01-25
• [Presentation] バビロンまでは何マイル？ ― コンパクト化の近似と集合論 (2012)
  • Author(s): 嘉田勝
  • Organizer: 第５９回トポロジーシンポジウム
  • Place of Presentation: 佐賀大学理工学部
  • Invited
• [Presentation] 距離関数の順序構造とGalois-Tukey connection (2012)
  • Author(s): 嘉田勝，吉信康夫
  • Organizer: 日本数学会2012年度秋季総合分科会
  • Place of Presentation: 九州大学伊都キャンパス
• [Presentation] A technique for proving preservation of topological properties under forcing extensions (2012)
  • Author(s): 嘉田勝
  • Organizer: RIMS研究集会 強制法による拡大と巨大基数
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] 点列の集合への収束と強制拡大 (2012)
  • Author(s): 岩佐明，嘉田勝，加茂静夫
  • Organizer: 2012 General Topology シンポジウム
  • Place of Presentation: 神戸大学
• [Presentation] Preservation of the Lindelof property and infinite games on posets. (2011)
  • Author(s): Masaru Kada.
  • Organizer: TOPOSYM 2011 (11th Topological Symposium).
  • Place of Presentation: Prague, Czech Republic
  • Year and Date: 2011-08-09
• [Presentation] Preservation of the Lindelof property and infinite games on posets (2011)
  • Author(s): Masaru Kada
  • Organizer: TOPOSYM 2011 (11th Topological Symposium)
  • Place of Presentation: プラハ(チェコ共和国)
  • Year and Date: 2011-08-08
• [Presentation] Infinite games for preserving topological covering properties. (2011)
  • Author(s): Masaru Kada
  • Organizer: BLAST 2011
  • Place of Presentation: Laurence,Kansas, USA
  • Year and Date: 2011-06-04
• [Presentation] Infinite games for preserving topological covering properties (2011)
  • Author(s): Masaru Kada
  • Organizer: BLAST 2011
  • Place of Presentation: University of Kansas(アメリカ)
  • Year and Date: 2011-06-04
• [Presentation] How many miles to βX, after all?. (2010)
  • Author(s): 嘉田勝 , 友安一夫 , 吉信康夫
  • Organizer: 2010年度General Topologyシンポジウム
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-12-20
• [Presentation] How many miles to β X, after all? (2010)
  • Author(s): 嘉田勝, 友安一夫, 吉信康夫
  • Organizer: 2010年度General Topologyシンポジウム
  • Place of Presentation: 筑波大学(茨城県)
  • Year and Date: 2010-12-20
• [Presentation] 良い強制拡大は,位相空間の良い性質を壊さない (2010)
  • Author(s): 嘉田勝
  • Organizer: 数学基礎論若手の会2010
  • Place of Presentation: 愛知県青年の家(愛知県)
  • Year and Date: 2010-11-19
• [Presentation] Remarks on Scheepers' theorem on the cardinality of Lindelof spaces (2010)
  • Author(s): 嘉田勝
  • Organizer: 大きな無限と小さな無限の相互関係(RIMS 研究集会)
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-10-25
• [Presentation] Remarks on Scheepers' theorem on the cardinality of Lindelof spaces (2010)
  • Author(s): 嘉田勝
  • Organizer: 大きな無限と小さな無限の相互関係(RIMS研究集会)
  • Place of Presentation: 京都大学数理解析研究所(京都府)
  • Year and Date: 2010-10-25
• [Presentation] コーエン強制,ランダム強制に関する位相空間の性質の保存 (2010)
  • Author(s): 嘉田勝
  • Organizer: 一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用(RIMS 研究集会)
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-10-14
• [Presentation] コーエン強制,ランダム強制に関する位相空間の性質の保存 (2010)
  • Author(s): 嘉田勝
  • Organizer: 一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用(RIMS研究集会)
  • Place of Presentation: 京都大学数理解析研究所(京都府)
  • Year and Date: 2010-10-14
• [Presentation] Preserving topological covering properties under forcing extensions (2010)
  • Author(s): Masaru Kada
  • Organizer: International Conference Japan-Mexico on Topology and its Applications (V JAMEX)
  • Place of Presentation: Colima, Mexico
  • Year and Date: 2010-09-27
• [Presentation] Preserving topological covering properties under forcing extensions (2010)
  • Author(s): Masaru Kada
  • Organizer: International Conference Japan-Mexico on Topology and its Applications(V-JAMEX)
  • Place of Presentation: Universidad de Colima(メキシコ)
  • Year and Date: 2010-09-27
• [Presentation] Preserving the Lindelof property under forcing extensions (2010)
  • Author(s): 嘉田勝
  • Organizer: 第45回位相空間論シンポジウム
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-06-05
• [Presentation] Preserving the Lindelof property under forcing extensions (2010)
  • Author(s): 嘉田勝
  • Organizer: 第45回位相空間論シンポジウム
  • Place of Presentation: 大阪府立大学(大阪府)
  • Year and Date: 2010-06-05
• [Presentation] Preserving the Lindelof property under forcing extensions (2010)
  • Author(s): Masaru Kada
  • Organizer: Boise Extravaganza in Set Theory 19 (BEST 2010).
  • Place of Presentation: Boise, Idaho, USA
  • Year and Date: 2010-03-28
• [Presentation] Preserving the Lindelof property under forcing extensions (2010)
  • Author(s): Masaru Kada
  • Organizer: Boise Extravaganza in Set Theory 19 (BEST2010)
  • Place of Presentation: ボイジー州立大学(アメリカ)
  • Year and Date: 2010-03-28
• [Presentation] Preserving the Lindeof property under forcing extensions. (2010)
  • Author(s): Masaru Kada
  • Organizer: 44th Annual Spring Topology and Dynamics Conference
  • Place of Presentation: Starkville, Mississippi, USA
  • Year and Date: 2010-03-18
• [Presentation] Preserving the Lindelof property under forcing extensions (2010)
  • Author(s): Masaru Kada
  • Organizer: 44th annual Spring Topology and Dynamics Conference 2010
  • Place of Presentation: ミシシッピ州立大学(アメリカ)
  • Year and Date: 2010-03-18
• [Presentation] Galois-Tukey connections involving sets of metrics. (2009)
  • Author(s): Masaru Kada
  • Organizer: 24th Summer Conference on Topology and Its Applications.
  • Place of Presentation: Brno, Czech Republic.
  • Year and Date: 2009-07-16
• [Presentation] Galois-Tukey connections involving sets of metrics (2009)
  • Author(s): 嘉田勝
  • 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
• [Remarks]
  • URL: http://www.mi.s.osakafu-u.ac.jp/~kada/kaken2009/
• [Remarks] 集合論的手法による位相空間論の新たな展開
  • URL: http://www.mi.s.osakafu-u.ac.jp/~kada/kaken2009/
• [Remarks] 研究代表者作成webページ
  • URL: http://www.mi.s.osakafu-u.ac.jp/~kada/kaken2009/
• [Remarks] 研究代表者作成webページ
  • URL: http://www.mi.s.osakafu-u.ac.jp/~kada/kaken2009/
• [Remarks] 研究代表者作成webページ
  • URL: http://www.mi.s.osakafu-u.ac.jp/~kada/kaken2009/