Topology of hyperspaces, mapping spaces and universal spaces

超空间、映射空间和通用空间的拓扑

基本信息

批准号：
17540061
负责人：
SAKAI Katsuro
金额：
$ 2.3万
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：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

To achieve three objects mentioned at the beginning of this project, the head investigator have been making researches in cooperation with investigators and invited W. Kubis from Poland and T. Banakh from Ukraine to do joint works and to exchange information. Finally, we obtained many good results. Concerning the first object to specify under what conditions and to what spaces each of various hyperspaces is homeomorphic (even in non-separable case), by many joint works conducted by the head, we had such results as: specifying hyperspaces on Banach spaces with the Wijsman topology; finding conditions of metric spaces whose hyperspaces of closed sets are ANR's; proving that the hyperspace of closed convex sets in a normed space is an ANR with respect to Hausdorff uniformity and Attouch-Wets topology and for a finite-dimensional normed space it is homeomorphic to the product of the base space and the Hilbert cube; specifying hyperspaces consisting of compacta of various types; proving tha … More t the hyperspaces of bounded closed sets in the space of irrationals and the Noebeling spaces. Concerning the second object to find mapping spaces being infinite-dimensional manifold and to clarify their topological structure, Yagasaki classified the connected component of the inclusion in the space of embeddings of a subpolyhedron into a surface and generalized Berlange's result on the group of measure-preserving homeo-morphisms to non-compact case. The head collaborated Uehara on clarifying topological structure of the space of lower semi-continuous functions. Moreover, in the joint work with Banakh, Mine and Yagasaki, he proved that the homeomorphism group of non-compact surfaces with the Whitney topology can be embedded in the product of the Hilbert space and the direct limit of Euclidean spaces as open sets. Concerning the object to enrich studies on non-separable infinite-dimensional universal spaces and to complete the proof of characterization of Noebeling spaces, the latter was done by Nagorko and we could not give any contribution but the head and Mine could obtain the classification theorem on open sets in LF-spaces, which can be a foothold on studying LF-manifolds. Less

为了提及该项目的三个对象，首席调查员押注了来自波兰的W. kubis和来自乌克兰的T. Banakh进行联合工作并交换信息。对于同型寓言案例，各种超级空间的spach是由头部进行的许多联合作品的结果，我们取得了这样的结果：在Wijsman拓扑中指定在Banach空间上的超级空间；对于基本空间和Hilbert Cube的产物而言，对拓扑的拓扑和有限的空间是同构的；第二个对象是映射空间是无限的二歧管，并阐明了其在表面嵌入的空间中包含的拓扑结构，并在表面上的berlange嵌入到了对非compactact案件的概述Head与Banakh，Mine和Yagasaki的较低半连续功能空间的澄清结构合作。欧几里得空间作为开放式集合的直接。 LF空间中的集合可以是研究LF-manifolds的父亲