Research on "Classification of filters and subsets of reals with respect to selector, and convergence properties of hyperspacea"

“关于选择器的滤波器和实数子集的分类以及超空间的收敛特性”研究

• 批准号: 15540125
• 负责人: NOGURA Tsugunori
• 金额: $ 2.11万
• 依托单位: Ehime University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540125/
• 关键词: Selector; Hyperspace; Fell topology; Dimension; Vietoris topology; Countably compact; 連続選択関数; Ginsburg's question; 積空間; 可算コンパクト性; 擬コンパクト性; Ginsburg's problem

We investigate topological properties of spaces which admit continuous (weak)selction and also the relationship between topological properties of hyperspaces and that of base spaces, especially convergence properties. The main results obtained by our project are as follows ;(1)If X is homogeneous space, then countable (pseudo) compactness of hyperspace implies that of countable product of X. This gives a partial solution of Ginsburgs problem.(2)We establishe that topologically welorderability of base space is equivalent to the existence of Fell continuous selection.(3)There exists a space which admit a continuous weal selection but small inductive dimension can be taken any natural number.

我们研究了空间的拓扑特性，这些拓扑特性允许连续的（弱）连续（较弱）的连续性以及高空空间的拓扑特性与基本空间的拓扑特性之间的关系，尤其是收敛性能。我们项目获得的主要结果如下：（1）如果x是均匀的空间，那么高空空间的可占（伪）紧凑性意味着X的可计数产物。这给出了Ginsburgs问题的部分解决方案。（2）我们确定基本空间的基础空间与倒下的选择相等，但该空间的次数是持续的选择。维度可以占据任何自然数字。

项目成果

Non-normality numbers

非正态数

• 发表时间: 2003
• 期刊: Topology Proceedings 27
• 作者: S.Dolecki;T.Nogura;R.Peirone;M.Reed
• 通讯作者: M.Reed

Selection pointwise-maximal spaces

选择逐点最大空间

• 发表时间: 2005
• 期刊: Topology and its Applications 146
• 作者: V.Gutev;T.Nogura
• 通讯作者: T.Nogura

V.Gutev, T.Nogura: "Fell continuous selections and topologically well-orderable spaces"Mathematica. (印刷中).

V. Gutev、T. Nogura：“连续选择和拓扑良好有序空间”Mathematica（正在出版）。

Extensions of 2-point selections

2点选择的扩展

• 发表时间: 2008
• 期刊: New Zealand Journal of Mathematics 38
• 作者: S. Dolecki;H. Kunzi;T. Nogura;Toru Ohmoto;Jun O' Hara (今井の旧姓);D. Dikranjan; D. Shakhmatov;Jun O' Hara (今井の旧姓);K. Miyajima;Remi Langevin and Jun O'Hara;D. Dikranjan; D. Shakhmatov;H. Sainohira and Shoji Tsuboi;今井淳;S. Garcia-Ferreira; V. Gutev; T. Nogura
• 通讯作者: S. Garcia-Ferreira; V. Gutev; T. Nogura

Fell continuous selections and topologically well-orderable spaces

连续选择和拓扑有序空间

• 发表时间: 2004
• 期刊: Mathematika 51
• 作者: V.Gutev;T.Nogura
• 通讯作者: T.Nogura