Article
MSC:
54D15,
54D35,
54D40,
54D80,
54E35,
54G20 | MR 4577044 | Zbl 07729556 | DOI: 10.14712/1213-7243.2023.011
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Keywords:
Čech--Stone compactification; non-normality point; butterfly-point; countable $\pi$-weight
Čech--Stone compactification; non-normality point; butterfly-point; countable $\pi$-weight
Summary:
We discuss the following result of A. Szymański in ``Retracts and non-normality points" (2012), Corollary 3.5.: If $F$ is a closed subspace of $\omega ^{*}$ and the $\pi$-weight of $F$ is countable, then every nonisolated point of $F$ is a non-normality point of $\omega ^{*}$. We obtain stronger results for all types of points, excluding the limits of countable discrete sets considered in ``Some non-normal subspaces of the Čech--Stone compactification of a discrete space'' (1980) by A. Błaszczyk and A. Szymański. Perhaps our proofs look ``more natural in this area''.
References:
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