Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516948 | Topology and its Applications | 2005 | 26 Pages |
Abstract
Let X be a separable metric space. By CldW(X), we denote the hyperspace of non-empty closed subsets of X with the Wijsman topology. Let FinW(X) and BddW(X) be the subspaces of CldW(X) consisting of all non-empty finite sets and of all non-empty bounded closed sets, respectively. It is proved that if X is an infinite-dimensional separable Banach space then CldW(X) is homeomorphic to (â) the separable Hilbert space â2 and FinW(X)âBddW(X)ââ2Ãâ2f, where â2f={(xi)iâNââ2|xi=0 except for finitely many iâN}. Moreover, we show that if the complement of any finite union of open balls in X has only finitely many path-components, all of which are closed in X, then FinW(X) and CldW(X) are ANR's. We also give a sufficient condition under which FinW(X) is homotopy dense in CldW(X).
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
WiesÅaw KubiÅ, Katsuro Sakai, Masato Yaguchi,