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Proceedings of the American Mathematical Society

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

 

 

On precompact (quasi-) uniform structures


Author: P. Th. Lambrinos
Journal: Proc. Amer. Math. Soc. 62 (1977), 365-366
MSC: Primary 54E15
MathSciNet review: 0428292
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Abstract: The following are shown:

(1) The subbasis theorem on precompactness does not hold even in uniform spaces.

(2) The supremum of (even finitely many) precompact quasi-uniform structures is not necessarily precompact.

(3) A compact quasi-uniform space is not necessarily totally bounded.

These results contradict corresponding assertions in the literature.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0428292-0
Keywords: Precompact (quasi-) uniform structures
Article copyright: © Copyright 1977 American Mathematical Society