U(X) as a ring for metric spaces X

In this short paper, we will show that the space of real valued uniformly continuous functions defined on a metric space (X,d) is a ring if and only if every subset A ? X has one of the following properties: ? A is Bourbaki-bounded, i.e., every uniformly continuous function on X is bounded on A. ? A...

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Bibliographic Details
Published in:Filomat 2017, Vol.31 (7), p.1981-1984
Main Author: Cabello, Sànchez
Format: Article
Language:English
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Summary:In this short paper, we will show that the space of real valued uniformly continuous functions defined on a metric space (X,d) is a ring if and only if every subset A ? X has one of the following properties: ? A is Bourbaki-bounded, i.e., every uniformly continuous function on X is bounded on A. ? A contains an infinite uniformly isolated subset, i.e., there exist ? > 0 and an infinite subset F ? A such that d(a,x) ? ? for every a ? F, x ? X n \{a}. nema
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1707981C