## Sergei Logunov

*On Szymański theorem on hereditary normality of \beta\omega*

Comment.Math.Univ.Carolin. 63,4 (2022) 507-512.**Abstract: **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".

**Keywords:** Čech-Stone compactification; non-normality point; butterfly-point; countable \pi-weight

**DOI:** DOI 10.14712/1213-7243.2023.011

**AMS Subject Classification:** 54D15 54D35 54D40 54D80 54E35 54G20

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