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

为了实现该项目开头提到的三个对象，首席调查员一直在与调查人员合作进行研究，并邀请来自波兰的W. Kubis和来自乌克兰的T. Banakh进行联合工作和交换信息。最后，我们获得了许多不错的结果。关于在哪个条件下以及在各个空间中指定的第一个对象都是同构的（即使在不可分割的情况下），这是由头部进行的许多联合作品，我们取得了这样的结果：指定与Wijsman拓扑的Banach空间上的超空间；查找封闭套件超级空间的度量空间的条件是ANR的。证明在标准空间中的封闭凸的超空间是关于Hausdorff均匀性和Attouch-wets拓扑的ANR，并且对于有限的差异空间，它对基本空间和Hilbert Cube的产物是同质的；指定由各种类型的紧凑型组成的超级空间；证明……在非理性和诺贝尔空间的空间中，有限封闭集的超空间。 Yagasaki对第二个对象发现映射空间是无限的二维歧管，并阐明其拓扑结构，并将其纳入了附属物的连接组件中，将亚电体的包合物与表面贝尔兰格的包包式嵌入空间中，并将其推广到量子标准的势力绩效案例中。头部与Uehara合作，阐明了较低半连续功能的空间的拓扑结构。此外，在与Banakh，Mine和Yagasaki的联合合作中，他证明了与惠特尼拓扑结构的非紧凑表面的同构群可以嵌入Hilbert Space的产物中，以及欧几里得空间的直接限制。关于富集对非分离无限维通用空间的研究并完成Noebeling空间表征证明的对象，后者是由Nagorko进行的，我们无法做出任何贡献，但是头部和我的头部和我的头部都可以在LF空间中获得开放式定理，这可以是研究LF-lf-lf-manifolds的foothold ford。较少的