Classification of Higher dimensional Erdos spaces by singular selectors

• Project/Area Number: 22540137
• 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: Ehime University
• Principal Investigator: NOGURA Tsugunori 愛媛大学, 名誉教授 (00036419)
• Co-Investigator(Renkei-kenkyūsha): SHAKHMATOV Dmitri 愛媛大学, 理工学研究科, 教授 (90253294)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 順序数空間 / 連続弱選択関数 / 超空間 / 次元 / セレクター / 積空間 / 順序付け可能 / 順序付け可能性 / 順序 / 弱順序

Research Abstract

It is well known that topologies generated by continuous weak selections are weaker than the original topologies. We call a space is CWS if the topology is generated by continuous weak selections. We have established the fundamental properties of CWS spaces and calculate the CWS numbers of several examples. Also we investigate the weak orderability of product spaces. As applications we show that if the product of a GO-space and a first countable space is weakly orderable, then the GO-space must be hereditarily paracompact. Also we have shown that a pseudocompact space without isolated point is homeomorphic to the Cantor set if and only ifits cube X×X×X is weakly orderable.

Research Products

• [Journal Article] Topologies generated by weak selection topologies (2013)
  • Author(s): Salvador Garcia-Ferreira
  • Journal Title: Houston J. Math. Volume: -
  • Peer Reviewed
• [Journal Article] Continuous weak selections for products (2013)
  • Author(s): Salvador Garcia-Ferreira
  • Journal Title: Topology Appl. Volume: -
  • Peer Reviewed
• [Journal Article] On the existence of kings in continuous tournaments (2012)
  • Author(s): Nagao, M.; Shakhmatov D.
  • Journal Title: Topology Appl Volume: 159 Pages: 3089-3096
  • Peer Reviewed
• [Journal Article] Quasi convexity dense and suitable sets in the arc component of a compact group (2012)
  • Author(s): Dikaranjan D.; Shakhmatov D.
  • Journal Title: Math. Nachr Volume: 285 Pages: 476-485
  • Peer Reviewed
• [Journal Article] A Kronecker-Weyl theorem fpr subsets of abelian groups (2011)
  • Author(s): Dikranjan D.;Shakhmatov D.
  • Journal Title: Adv. Math. Volume: 226 Pages: 4776-4795
• [Journal Article] Productivity of sequences with respect to a given weight function (2011)
  • Author(s): Dikranjan D.; Shakhmatov D.; Spevak J
  • Journal Title: Topology Appl Volume: 158 Pages: 298-324
  • Peer Reviewed
• [Journal Article] Weak orderability of topological spaces (2010)
  • Author(s): Gutev V.; Nogura T
  • Journal Title: Topology Appl Volume: 157 Pages: 1249-1274
  • Peer Reviewed
• [Journal Article] Set-maximal selections (2010)
  • Author(s): Gutev V.; Nogura, T
  • Journal Title: Topology Appl. Volume: 157 Pages: 53-61
  • Peer Reviewed
• [Journal Article] The Markov-Zariski topology of abelian group (2010)
  • Author(s): Dikranjan D.; Shakhmatov, D
  • Journal Title: J. Algebra Volume: 324 Pages: 1125-1158
  • Peer Reviewed
• [Journal Article] Hewitt-Marczewski- Pondiczery type theorem for abelian groups and Markov's potential density (2010)
  • Author(s): Dikranjan D.; Shakhmatov D
  • Journal Title: Proc. Amer. Math. Soc. Volume: 138 Pages: 2979-2990
  • Peer Reviewed
• [Journal Article] Group valued continuous functions with the topology of pointwise convergence (2010)
  • Author(s): Shakhmatov D.; Spevak J
  • Journal Title: Topology Appl Volume: 157 Pages: 1518-1540
  • Peer Reviewed
• [Journal Article] Weak orderability of topological spaces (2010)
  • Author(s): V.Gutev, T.Nogura
  • Journal Title: Topology and its Applications Volume: 157 Pages: 1249-1274
  • Peer Reviewed
• [Journal Article] Set-maximal selections (2010)
  • Author(s): V.Gutev, T.Nogura
  • Journal Title: Topology ans its Applications Volume: 157 Pages: 53-61
  • Peer Reviewed
• [Journal Article] Topologies generated by weak selection topologies
  • Author(s): Garcia-Ferreira, S; Miyazaki, K; Nogura T.; Tomita, A. H.
  • Journal Title: Houston J. Math. Volume: (accepted)
  • Peer Reviewed
• [Journal Article] Weakly orderability for products
  • Author(s): Garcia-Ferreira, S; Miyazaki, K; Nogura, T
  • Journal Title: Topology Appl. Volume: (accepted)
  • Peer Reviewed
• [Presentation] Topologies generated by weak selection topologies (2012)
  • Author(s): Nogura T
  • Organizer: International conference of Topology and related topics
  • Place of Presentation: 南京,(中国)
• [Presentation] Graphtheoretic aspect of continuous weak selection (2012)
  • Author(s): Shakhmatov D
  • Organizer: IVth Workshop on Coverings, Selections and Games in Topology
  • Place of Presentation: Caserta(Italy)
• [Presentation] Metrizability of compact groups via conditions on their dense subgroups (2012)
  • Author(s): Shakhmatov D
  • Organizer: TOPOSYM 2011
  • Place of Presentation: Prague(Czech Republic)
• [Presentation] Topologies generated by weak selection topologies (2012)
  • Author(s): Tsugunori Nogura
  • Organizer: International conference of topology and related topics
  • Place of Presentation: 南京大学（中国）
  • Invited
• [Presentation] Two decades of pseudocompact group topologization problem (2010)
  • Author(s): Shakhmatov D
  • Place of Presentation: Barcelona (Spain)
• [Presentation] Topological properties of the Markov-Zariski topology of an abelian group (2010)
  • Author(s): Shakhmatov D
  • Organizer: 2010 International conference on Topology and its Applications
  • Place of Presentation: Nafpaktos (Greece)