Vol. 111, No. 1, 1984

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Cauchy spaces with regular completions

Darrell Conley Kent and Gary Douglas Richardson

Vol. 111 (1984), No. 1, 105–116

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
Received: 15 March 1982
Published: 1 March 1984
Darrell Conley Kent
Gary Douglas Richardson