Article
MSC:
54D15,
54D35,
54D40,
54D80,
54E35,
54G20 | MR 4445740 | Zbl 07584116 | DOI: 10.14712/1213-7243.2022.004
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Keywords:
non-normality point; Čech--Stone compactification; Tychonoff product; Suslin number
non-normality point; Čech--Stone compactification; Tychonoff product; Suslin number
Summary:
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.
References:
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