Geodesic
On Szymański theorem on hereditary normality of $\beta\omega$
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 4, pp. 507-512 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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''.
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''.
DOI : 10.14712/1213-7243.2023.011
Classification : 54D15, 54D35, 54D40, 54D80, 54E35, 54G20
Keywords: Čech--Stone compactification; non-normality point; butterfly-point; countable $\pi$-weight 
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Logunov, Sergei. On Szymański theorem on hereditary normality of $\beta\omega$. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 4, pp. 507-512. doi: 10.14712/1213-7243.2023.011

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