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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Product spaces in locales


Author: John Isbell
Journal: Proc. Amer. Math. Soc. 81 (1981), 116-118
MSC: Primary 54B10
MathSciNet review: 589150
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Abstract: The embedding of sober spaces in locales preserves products $ X \times Y$ where $ X$ is quasi-locally compact. A completely regular space $ X$ has this preservation property, for all $ Y$, if and only if $ X$ is a complemented sublocale of a compact space. Equivalently, every closed subset of $ X$ is locally compact somewhere.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0589150-5
PII: S 0002-9939(1981)0589150-5
Keywords: Locale, quasi-locally compact
Article copyright: © Copyright 1981 American Mathematical Society