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Proceedings of the American Mathematical Society

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

 

 

A note on uniform paracompactness


Author: Michael D. Rice
Journal: Proc. Amer. Math. Soc. 62 (1977), 359-362
MSC: Primary 54E15; Secondary 54D20
DOI: https://doi.org/10.1090/S0002-9939-1977-0436085-3
MathSciNet review: 0436085
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Abstract: Three possible definitions for the paracompactness of a uniform space are presented and shown to be equivalent. A locally compact uniform space is shown to be uniformly paracompact if and only if it is uniformly locally compact. The set of points of a uniformly paracompact metric space that admit no compact neighborhood is shown to be compact; hence a metric topological group is uniformly paracompact if and only if it is locally compact.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0436085-3
Keywords: Uniformly locally finite open cover, paracompact, uniformly paracompact, locally compact, uniformly locally compact
Article copyright: © Copyright 1977 American Mathematical Society