Article
| Title: | On butterfly-points in $\beta X$, Tychonoff products and weak Lindelöf numbers (English) |
| Author: | Logunov, Sergei |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 63 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 379-383 |
| Summary lang: | English |
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| Category: | math |
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| 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. (English) |
| Keyword: | Butterfly-point |
| Keyword: | non-normality point |
| Keyword: | Čech--Stone compactification |
| Keyword: | Tychonoff product |
| Keyword: | weak Lindelöf number |
| MSC: | 54D15 |
| MSC: | 54D35 |
| MSC: | 54D40 |
| MSC: | 54D80 |
| MSC: | 54E35 |
| MSC: | 54G20 |
| idZBL: | Zbl 07655807 |
| idMR: | MR4542796 |
| DOI: | 10.14712/1213-7243.2022.023 |
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| Date available: | 2023-02-01T12:12:05Z |
| Last updated: | 2023-04-20 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151483 |
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