A remark on R. G. Woods' paper 'The minimum uniform compactification of a metric space'

摘要

A question raised in R. G. Woods' paper has a simple solution. The minimum uniform compactification uX of a metric space X is the smallest compactification of X such that every bounded real-valued Tini-formly continuous function on X has a continuous extension to uAr. Two subsets of X are distant iff they have disjoint closures in uX. Woods proves that vM. is a perfect compactification of M and leaves the case of uRn open.