Article
| Title: | On $\lambda$-Kunen points and $\beta$-normality of $\beta X\setminus \{p\}$ (English) |
| Author: | Logunov, Sergei |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 66 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 121-126 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We show that every point of the remainder $\beta X\setminus X$ of the Čech--Stone compactification $\beta X$ of any metrizable crowded space $X$ is a ``$\lambda$-Kunen" point for some regular cardinal $\lambda$. As a consequence we show that $\beta X \setminus \{p\}$ is not $\beta$-normal in the sense of result published in the paper On $\alpha$-normal and $\beta$-normal spaces (2021) by A. V. Arhangel'skii and L. Ludwig and, it explicitly indicate closed subsets of $\beta X \setminus \{p\}$ that cannot be ``$\beta$-separated". (English) |
| Keyword: | Kunen point |
| Keyword: | $\beta$-normality |
| Keyword: | Čech--Stone compactification |
| Keyword: | metrizable crowded space |
| MSC: | 54D15 |
| MSC: | 54D35 |
| MSC: | 54D40 |
| MSC: | 54D80 |
| MSC: | 54E35 |
| MSC: | 54G20 |
| DOI: | 10.14712/1213-7243.2026.001 |
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| Date available: | 2026-05-15T05:58:41Z |
| Last updated: | 2026-05-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153605 |
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| Reference: | [1] Arhangel'skii A. V., Ludwig L.: On $\alpha$-normal and $\beta$-normal spaces.Comment. Math. Univ. Carolin. 42 (2001), no. 3, 507–519. |
| Reference: | [2] Logunov S. A.: On non-normality points and metrizable crowded spaces.Comment. Math. Univ. Carolin. 48 (2007), no. 3, 523–527. |
| Reference: | [3] Logunov S. A.: Non-normality points and nice spaces.Comment. Math. Univ. Carolin. 62 (2021), no. 3, 383–392. |
| Reference: | [4] Terasawa J.: $\beta X-\{p\}$ are non-normal for non-discrete spaces $X$.Topology Proc. 31 (2007), no. 1, 309–317. |
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