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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On Biesterfeldt's completion axiom spaces


Author: R. J. Gazik
Journal: Proc. Amer. Math. Soc. 52 (1975), 401-405
MSC: Primary 54A20; Secondary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1975-0375201-7
MathSciNet review: 0375201
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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0375201-7
Keywords: Uniform convergence spaces, completions of uniform convergence spaces, Completion Axiom, uniformly regular and uniformly strict completions
Article copyright: © Copyright 1975 American Mathematical Society

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