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Proceedings of the American Mathematical Society

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

 

 

Countable metacompactness in $ \Psi$-spaces


Author: Paul Szeptycki
Journal: Proc. Amer. Math. Soc. 120 (1994), 1241-1246
MSC: Primary 54D15; Secondary 03E05, 04A20, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1994-1169890-9
MathSciNet review: 1169890
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Abstract: We prove under a variety of assumptions including $ \mathfrak{c} = {\aleph _2}$ that, for every maximal almost disjoint family $ \mathcal{A}$ of countable subsets of $ {\omega _1},\;\Psi (\mathcal{A})$ is not countably metacompact. In addition, a first countable, countably metacompact, regular space with a closed discrete set which is not a $ {G_\delta }$ is constructed from the mutually consistent assumptions that $ \mathfrak{b} = {\omega _1}$ and there can exist a Q-set.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1169890-9
Keywords: Countably metacompact, perfect, mad, unbounded, Q-set
Article copyright: © Copyright 1994 American Mathematical Society