Abstract:Given uniformly homeomorphic metric spaces X and Y , it is proved that the hyperspaces C(X) and C(Y ) are uniformly homeomorphic, where C(X) denotes the collection of all nonempty closed subsets of X, and is endowed with Hausdorff distance. Gerald Beer has proved that the hyperspace C(X) is Atsuji when X is either compact or uniformly discrete. An Atsuji space is a generalization of compact metric spaces as well as of uniformly discrete spaces. In this article, we investigate the space C(X) when X is Atsuji, a… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.