The minimum uniform compactification of a metric space
نویسنده
چکیده
It is shown that associated with each metric space (X, d) there is a compactification udX of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of udX are presented, and a detailed study of the structure of udX is undertaken. This culminates in a topological characterization of the outgrowth udR \ R, where (R, d) is Euclidean n-space with its usual metric.
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