Regular completions of Cauchy spaces

Darrell Kent, Gary Richardson
1974 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 convergence
more » ... ace and the set of ordered precompact Cauchy structures inducing the given convergence structure.
doi:10.2140/pjm.1974.51.483 fatcat:24hxtlh2wbae3m4o7hjbe2cbv4