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

• 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; 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

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. 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在同构和嵌入的空间上（Yagasaki）；（5）Peano和Anr Continua（Yagasaki）的空间；（6）ANR（Sakai）的特征。非压缩度量空间（Sakai-Kurihara-Yang）.2。 Menger流形和N形理论。在这一部分中，我们在以下研究中有许多结果：（1）Menger流形动态（Kato-Kawamura-tuncali-tymchatyn）;（2）同源型Menger compacta的同态层面的维度（Kawamura-brechner）（Kawamura-Brechner）; （Kawamura）;（4）在Menger Curve（Kawamura）中的集体行动；（5）通用空间的应用，用于一类公开图像的封闭图像（kawamura-tuda）；（6）对适当的N型理论（Sakai-Akaike）的研究；（7）强烈的N-Shape（Sakai-ape）（7）强烈的N-Shape（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。