On Szymański theorem on hereditary normality of
Commentationes Mathematicae Universitatis Carolinae (2022)
- Volume: 62 63, Issue: 4, page 507-512
- ISSN: 0010-2628
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topLogunov, Sergei. "On Szymański theorem on hereditary normality of $\beta \omega $." Commentationes Mathematicae Universitatis Carolinae 62 63.4 (2022): 507-512. <http://eudml.org/doc/299044>.
@article{Logunov2022,
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”.},
author = {Logunov, Sergei},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Čech–Stone compactification; non-normality point; butterfly-point; countable $\pi $-weight},
language = {eng},
number = {4},
pages = {507-512},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Szymański theorem on hereditary normality of $\beta \omega $},
url = {http://eudml.org/doc/299044},
volume = {62 63},
year = {2022},
}
TY - JOUR
AU - Logunov, Sergei
TI - On Szymański theorem on hereditary normality of $\beta \omega $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 4
SP - 507
EP - 512
AB - 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”.
LA - eng
KW - Čech–Stone compactification; non-normality point; butterfly-point; countable $\pi $-weight
UR - http://eudml.org/doc/299044
ER -
References
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