Countable metacompactness in Ψ-spaces

Szeptycki, Paul

doi:10.1090/S0002-9939-1994-1169890-9

Countable metacompactness in $\Psi$-spaces
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by Paul Szeptycki

Proc. Amer. Math. Soc. 120 (1994), 1241-1246

DOI: https://doi.org/10.1090/S0002-9939-1994-1169890-9

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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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