Induced Homeomorphism and Atsuji Hyperspaces

Given uniformly homeomorphic metric spaces $$X$$ and $$Y$$ , it is proven that hyperspaces $$C(X)$$ $$C(Y)$$ are homeomorphic, where denotes the collection of all nonempty closed subsets endowed with Hausdorff distance. Gerald Beer has proved hyperspace an Atsuji space when either compact or discrete. An a generalization as well discrete spaces. In this paper, we investigate space, class subspaces obtained. Using results, some fixed point results for continuous maps on