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Regular completions of Cauchy spaces
Pacific Journal of Mathematics
A uniform convergence space is a generalization of a uniform space. The set of all Cauchy filters of some uniform convergence space is called a Cauchy structure. We give necessary and sufficient conditions for the Cauchy structure of some totally bounded uniform convergence space to be precompact; i.e., have a regular completion. Also, it is shown that there is an isomorphism between the set of ordered equivalence classes of strict regular compactifications of a completely regular convergencedoi:10.2140/pjm.1974.51.483 fatcat:24hxtlh2wbae3m4o7hjbe2cbv4