On Biesterfeldt’s completion axiom spaces

Gazik, R. J.

doi:10.1090/S0002-9939-1975-0375201-7

On Biesterfeldt’s completion axiom spaces
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by R. J. Gazik PDF

Proc. Amer. Math. Soc. 52 (1975), 401-405 Request permission

Abstract:

It is proved that a Hausdorff, totally bounded Completion Axiom space is a uniform space. The method of proof shows that Hausdorff Completion Axiom spaces have completions (in the embedding sense) which are again Hausdorff Completion Axiom spaces; moreover these completions are uniformly regular, uniformly strict, and have the regular extension property.

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