Article
MSC:
54D15,
54D35,
54D40,
54D80,
54E35,
54G20 | MR 4542796 | Zbl 07655807 | DOI: 10.14712/1213-7243.2022.023
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Keywords:
Butterfly-point; non-normality point; Čech--Stone compactification; Tychonoff product; weak Lindelöf number
Butterfly-point; non-normality point; Čech--Stone compactification; Tychonoff product; weak Lindelöf number
Summary:
Let $X$ be the Tychonoff product $\prod _{\alpha <\tau}X_{\alpha}$ of $\tau$-many Tychonoff non-single point spaces $X_{\alpha}$. Let $p\in X^{*}$ be a point in the closure of some $G\subset X$ whose weak Lindelöf number is strictly less than the cofinality of $\tau$. Then we show that $\beta X\setminus \{p\}$ is not normal. Under some additional assumptions, $p$ is a butterfly-point in $\beta X$. In particular, this is true if either $X=\omega^{\tau}$ or $X=R^{\tau}$ and $\tau$ is infinite and not countably cofinal.
References:
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