Studies on Infinite-Dimensional Manifolds and Menger Manifolds, and their Applications

无限维流形和Menger流形的研究及其应用

基本信息

批准号：
10640060
负责人：
SAKAI Katsuro
金额：
$ 2.18万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640060/
关键词：
infinite-dimenisonal manifold absolute neighborhood retract (ANR)space of mappings hyperspace Menger manifold universal space proper n-shape theory strong n-shape theory Attouch-Wets位相 Fell位相 Hilbert空間 Hilbert cube strong universa

项目摘要

1. Infinite-Dimensional Manifolds and ANR Theory.In this part, we have many results in the following researches :(1) Characterizations of bitopological infinite-dimensional manifolds (Sakai-Banakh) ;(2) Studies on free topological semilattices (Sakai-Banakh) ;(3) Direct limits of Banach-Mazur compacta (Sakai-Kawamura-Banakh) ;(4) Studies on spaces of homeomorphisms and embeddings (Yagasaki) ;(5) Spaces of Peano and ANR continua (Yagasaki) ;(6) Characterizations of ANR's (Sakai).Recently, we have made some progress in the following two studies, whose development are expected :(7) Maps from mapping spaces to a hyperspaces (Yagasaki) ;(8) Hyperspaces of closed sets of non-compact metric spaces (Sakai-Kurihara-Yang).2. Menger Manifolds and n-Shape Theory.In this part, we have many results in the following researches :(1) Dynamics on Menger manifolds (Kato-Kawamura-Tuncali-Tymchatyn) ;(2) Dimension of the homeomorphism group of Menger compacta (Kawamura-Brechner) ;(3) Lusternik-Schnirelmann type invariants concerning Menger manifolds (Kawamura) ;(4) Groupe actions on Menger curve (Kawamura) ;(5) An application to a universal space for a class of closed images of metric spaces (Kawamura-Tuda) ;(6) Studies on proper n-shape theory (Sakai-Akaike) ;(7) Formulation of strong n-shape (Sakai-Iwamoto).3. In relation to this project, we invited Prof. Ageev (Belorussia) to learn about his research on the characterization of Nobeling spaces. Now, we are ready to work together with him, and further joint studies with him are expected.

1。无限维流形和ANR理论。在这一部分中，我们在以下研究中有许多结果：（1）比特比特型无限二维流形的特征（sakai-banakh）；（2）关于自由拓扑半层次的研究（sakai--- Banakh）;（3）Banach-Mazur Compacta（Sakai-Kawamura-Banakh）的直接限制；（4）对同质形态和嵌入空间（Yagasaki）的研究（Yagasaki）;（5）Peano和Anr Continua（6）（66））ANR（sakai）的特征。当然，我们在以下两项研究中取得了一些进展，其发展是可以预期的：（7）从映射空间到超空间（yagasaki）的地图；（8）非封闭空间的非封闭空间紧凑的度量空间（Sakai-Kurihara-Yang）.2。 Menger流形和N形理论。在这一部分，我们在以下研究中有许多结果：（1）Menger歧管（Kato-Kawamura-tuncali-tymchatyn）的动态；（2）同型Menger compacta的同态尺寸（（3）关于Menger歧管（Kawamura）的Lusternik-Schnirelmann类型不变的型（4）（4）对Menger Curve（Kawamura）的集体行动（5）（5）应用于通用空间的申请（Kawamura-tuda）;（6）关于适当的N形理论的研究（Sakai-Akaike）；（7）强烈的N形表达（Sakai-Iwamoto）.3。关于这个项目，我们邀请了Belorussia教授（Belorussia）教授了解他对诺贝林空间表征的研究。现在，我们准备与他一起工作，并期望与他进行进一步的联合研究。