Regular completions of Cauchy spaces

Darrell Conley Kent and Gary Douglas Richardson

Vol. 51 (1974), No. 2, 483–490

DOI: 10.2140/pjm.1974.51.483

Abstract

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 space and the set of ordered precompact Cauchy structures inducing the given convergence structure.

Mathematical Subject Classification 2000

Primary: 54A20

Secondary: 54D35

Milestones

Received: 29 November 1972

Revised: 22 August 1973

Published: 1 April 1974