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Proceedings of the American Mathematical Society
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 | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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  • [3] M. G. Murdeshwar and S. A. Naimpally, Quasi-uniform topological spaces, Noordhoff, Groningen, 1966. MR 35 #2267. MR 0211386 (35:2267)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0428292-0
PII: S 0002-9939(1977)0428292-0
Keywords: Precompact (quasi-) uniform structures
Article copyright: © Copyright 1977 American Mathematical Society