Vol. 94, No. 2, 1981

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A note on regular Cauchy spaces

Darrell Conley Kent

Vol. 94 (1981), No. 2, 333–339

A regular convergence space has both a finest and coarsest compatible regular Cauchy structure. The coarsest compatible regular Cauchy structure is complete if and only if the original space is Urysohn-closed; it is totally bounded if and only if the original space is almost topological. Minimal regular Cauchy spaces are characterized and, in the complete case, shown to be in one-to-one correspondence with the minimal regular convergence spaces. The noncomplete minimal regular regular Cauchy spaces do not have regular completions.

Mathematical Subject Classification 2000
Primary: 54A20
Received: 1 December 1978
Published: 1 June 1981
Darrell Conley Kent