On non-normality points, Tychonoff products and Suslin number
Commentationes Mathematicae Universitatis Carolinae (2022)
- Volume: 62 63, Issue: 1, page 131-134
- ISSN: 0010-2628
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topLogunov, Sergei. "On non-normality points, Tychonoff products and Suslin number." Commentationes Mathematicae Universitatis Carolinae 62 63.1 (2022): 131-134. <http://eudml.org/doc/299271>.
@article{Logunov2022,
abstract = {Let a space $X$ be Tychonoff product $\prod _\{\alpha <\tau \}X_\{\alpha \}$ of $\tau $-many Tychonoff nonsingle point spaces $X_\{\alpha \}$. Let Suslin number of $X$ be strictly less than the cofinality of $\tau $. Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification $\beta X$. In particular, this is true if $X$ is either $R^\{\tau \}$ or $\omega ^\{\tau \}$ and a cardinal $\tau $ is infinite and not countably cofinal.},
author = {Logunov, Sergei},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-normality point; Čech--Stone compactification; Tychonoff product; Suslin number},
language = {eng},
number = {1},
pages = {131-134},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On non-normality points, Tychonoff products and Suslin number},
url = {http://eudml.org/doc/299271},
volume = {62 63},
year = {2022},
}
TY - JOUR
AU - Logunov, Sergei
TI - On non-normality points, Tychonoff products and Suslin number
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 1
SP - 131
EP - 134
AB - Let a space $X$ be Tychonoff product $\prod _{\alpha <\tau }X_{\alpha }$ of $\tau $-many Tychonoff nonsingle point spaces $X_{\alpha }$. Let Suslin number of $X$ be strictly less than the cofinality of $\tau $. Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification $\beta X$. In particular, this is true if $X$ is either $R^{\tau }$ or $\omega ^{\tau }$ and a cardinal $\tau $ is infinite and not countably cofinal.
LA - eng
KW - non-normality point; Čech--Stone compactification; Tychonoff product; Suslin number
UR - http://eudml.org/doc/299271
ER -
References
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