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

 

The spaces which contain an $ S$-space


Author: W. F. Pfeffer
Journal: Proc. Amer. Math. Soc. 85 (1982), 659-660
MSC: Primary 54A25; Secondary 28A05, 54H05
MathSciNet review: 660624
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Abstract: Under the continuum hypothesis, we show that a $ {T_1}$-space $ X$ contains an $ S$-space if and only if there is an uncountable locally countable set $ E \subset X$ containing no Borel subset of $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660624-2
PII: S 0002-9939(1982)0660624-2
Keywords: Separable, Lindelöf, locally countable, Borel set, continuum hypothesis, Martin's axiom
Article copyright: © Copyright 1982 American Mathematical Society



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