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Proceedings of the American Mathematical Society

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

 
 

 

Countable paracompactness, normality, and Moore spaces


Author: Michael L. Wage
Journal: Proc. Amer. Math. Soc. 57 (1976), 183-188
MSC: Primary 54E30; Secondary 54D15, 04A15
DOI: https://doi.org/10.1090/S0002-9939-1976-0405364-7
MathSciNet review: 0405364
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Abstract: In this paper we show that $ {\text{MA}} + \neg{\text{CH}}$ implies that there exists a countably paracompact Moore space which is not normal. Further, if there is a model of set theory in which every countably paracompact Moore space is normal, then the normal Moore space conjecture is true in that model. Other examples are given, including a nonnormal space constructed with $ \diamond$ which is countably compact, $ {T_3}$, first countable, locally compact, perfect, and hereditarily separable.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0405364-7
Keywords: Countable paracompactness, Moore spaces, collectionwise normality, Martin's axiom
Article copyright: © Copyright 1976 American Mathematical Society

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