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More about metric spaces on which continuous functions are uniformly continuous

Published online by Cambridge University Press:  17 April 2009

Gerald Beer
Gerald Beer
Affiliation:
Department of Mathematics, California State University, Los Angeles, CA 90032, U.S.A.
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Abstract

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An Atsuji space is a metric space X such that each continuous function form X to an arbitrary metric space Y is uniformly continuous. We here present (i) characterizations of metric spaces with Atsuji completions; (ii) Cantor-type theorems for Atsuji spaces; (iii) a fixed point theorem for self-maps of an Atsuji space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 397 - 406
Copyright
Copyright © Australian Mathematical Society 1986

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