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On the topologies of the same class of homeomorphisms Shiau, Chyi

Abstract

Given a topological space (X,Ʊ), let H(X,Ʊ), be the class of all homeomorphisms of (XƱ ) onto itself. This paper is devoted to study the following problem posed by Everett and Ulam [1], [11] in 1948. When and how a new topology Ʋ can be constructed on X such that H(X,Ʊ) = H(X,Ʋ), i.e., these two topological spaces have exactly the same class of homeomorphisms. Some of the results obtained are original, and other results agree essentially with the work done previously by Yu-Lee Lee [5], [6], [7], [8], [9].

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