Construction of extender for continuous maps

• Project/Area Number: 23540100
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Takasaki City University of Economics
• Principal Investigator: Yamazaki Kaori 高崎経済大学, 経済学部, 教授 (80301076)
• Project Period (FY): 2011-04-28 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 拡張問題 / 内挿理論 / 拡張作用素 / 半連続写像 / 順序位相ベクトル空間 / 内挿定理 / 半連続関数 / way-below / 半順序集合 / 束 / 順序線形位相空間 / 順序ベクトル空間 / 内点 / 位相リース空間 / 単調可算パラコンパクト / 位相ベクトル束 / 挿入定理

Outline of Final Research Achievements

For extension problems of continuous maps, assignment for maps and insertion theory are studied. Monotone countable paracompactness is characterized by using assignment for maps with values in ordered topological vector spaces. Moreover, generalized Dowker-Katetov insertion theorems are also given for maps with the following ranges: (i) ordered topological vector spaces with positive interior points, (ii) bi-bounded complete and bicontinuous posets.

Research Products

• [Journal Article] Insertion of poset-valued maps with the way-below and -above relations (2018)
  • Author(s): Kaori Yamazaki
  • Journal Title: Topology and its Applications Volume: 未定
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Insertion theorems for maps to ordered topological vector spaces (2015)
  • Author(s): Kaori Yamazaki
  • Journal Title: Topology and its Applications Volume: 未定
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Monotone countable paracompactness and maps to topological vector spaces (2014)
  • Author(s): Kaori Yamazaki
  • Journal Title: Topology and its Applications Volume: 169 Pages: 51-70
  • DOI: 10.1016/j.topol.2014.02.032
  • Peer Reviewed
• [Journal Article] Monotone countable paracompactness and maps to ordered topological vector spaces (2013)
  • Author(s): Kaori Yamazaki
  • Journal Title: Topology and its Applications Volume: -
  • Peer Reviewed
• [Journal Article] The range of maps on classical insertion theorems (2011)
  • Author(s): Kaori Yamazaki
  • Journal Title: Acta Mathematical Hungarica Volume: 132 Issue: 1-2 Pages: 42-48
  • DOI: 10.1007/s10474-011-0096-0
  • Peer Reviewed
• [Presentation] Insertion of maps into bicontinuous lattices (2016)
  • Author(s): 山崎 薫里
  • Organizer: 2016年度ジェネラルトポロジーシンポジウム
  • Place of Presentation: 筑波大学（茨城県、つくば市）
  • Year and Date: 2016-12-08
• [Presentation] Insertion theorems for maps to ordered vector spaces (2014)
  • Author(s): 山崎 薫里
  • Organizer: 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: 2014-10-23
• [Presentation] 順序線形位相空間への半連続関数とその応用
  • Author(s): 山崎 薫里
  • Organizer: つくばセミナー
  • Place of Presentation: 筑波大学