On a hyperspace of compact subsets which is homeomorphic to a non-separable Hilbert space

2015/08/23 by Koshino, Katsuhisa
#57N20 #FOS: Mathematics #General Topology (math.GN) #Primary: 54B20 #Secondary: 54F65

paper · doi:10.48550/arxiv.1508.05557

Abstract

Let X be a metrizable space and \rm Comp(X) be the hyperspace consisting of non-empty compact subsets of X endowed with the Vietoris topology. In this paper, we give a necessary and sufficient condition on X for \rm Comp(X) to be homeomorphic to a non-separable Hilbert space. Moreover, we consider the topological structure of pair (\rm Comp(X),\rm Fin(X)) of hyperspaces of X and its completion X, where \rm Fin(X) is the hyperspace of non-empty finite sets in X.

Related

• Topological structures of hyperspaces of finite sets in non-separable metrizable spaces
• The compact strong Z-set property in a hyperspace of finite subsets
• The Vietoris hyperspace of finite sets of Erdős space
• The quasi-metrizability of hyperspaces
• Some generalized metric properties on hyperspaces with the Vietoris topology