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Proceedings of the American Mathematical Society

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

 

 

A characterization of real-compactness


Author: Li Pi Su
Journal: Proc. Amer. Math. Soc. 50 (1975), 412-418
MSC: Primary 54D60; Secondary 54E05
DOI: https://doi.org/10.1090/S0002-9939-1975-0391017-X
MathSciNet review: 0391017
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Abstract: Let $ \mathcal{Z}$ be a countably productive normal base in a Tychonoff space. We use proximity and construct a new Wallman-type realcompactification $ {\eta ^\ast }(\mathcal{Z})$ which is always realcompact. A Tychonoff space is realcompact iff it has a countably productive normal base $ \mathcal{Z}$ such that each $ \mathcal{Z}$-ultrafilter with weakly countable intersection property is fixed.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0391017-X
Keywords: Normal base, countably productive normal base, $ \mathcal{Z}$-ultrafilter, countable intersection property, weakly countable intersection property, strongly contained
Article copyright: © Copyright 1975 American Mathematical Society