Cauchy spaces with regular completions

Darrell Conley Kent and Gary Douglas Richardson

Vol. 111 (1984), No. 1, 105–116

DOI: 10.2140/pjm.1984.111.105

Abstract

A T₃ Cauchy space which has a regular completion is shown to have a T₃ completion, but an example shows that such Cauchy spaces need not have strict T₃ completions. Various conditions are found for the existence of T₃ completions and strict T₃ completions; for instance, every Cauchy-separated, locally compact, T₃ Cauchy space has a T₃ completion. Convergence spaces and topological spaces which have a coarsest compatible Cauchy structure with a strict T₃ completion are characterized, as are those spaces for which every compatible T₃ Cauchy structure has a T₃ completion.

Mathematical Subject Classification 2000

Primary: 54A20

Secondary: 54E15

Milestones

Received: 15 March 1982

Published: 1 March 1984