Abstract
Following Albert Edrei [1], if X is a compact metric space with metric p, f is a mapping of X onto X, and xEX, then x is said to be a point of contraction under f relative to X provided that there is a positive number ,(x) such that if yzX and p(x, y) <,I(x), then p[f (x), f(y) ] < p(x, y). Further, if each point of X is a point of contraction under f relative to X, f will be said to be a local contraction of X. Edrei posed the following question: if X is a compact metric space and f is a contraction of X onto X, is f a local isometry? The purpose of this paper is to answer this question in the negative.
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