Induced Homeomorphism and Atsuji Hyperspaces.

Given uniformly homeomorphic metric spaces and , it is proven that hyperspaces and are uniformly homeomorphic, where denotes the collection of all nonempty closed subsets of , and is endowed with Hausdorff distance. Gerald Beer has proved that hyperspace is an Atsuji space when 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 paper, we investigate space when is an Atsuji space, and a class of Atsuji subspaces of is obtained. Using the results, some fixed point results for continuous maps on Atsuji spaces are obtained. [ABSTRACT FROM AUTHOR]