Article
| Title: | $C^*$-points vs $P$-points and $P^\flat$-points (English) |
| Author: | Martinez, Jorge |
| Author: | McGovern, Warren Wm. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 63 |
| Issue: | 2 |
| Year: | 2022 |
| Pages: | 245-259 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | In a Tychonoff space $X$, the point $p\in X$ is called a $C^*$-point if every real-valued continuous function on $C\smallsetminus \{p\}$ can be extended continuously to $p$. Every point in an extremally disconnected space is a $C^*$-point. A classic example is the space ${\bf W}^*=\omega_1+1$ consisting of the countable ordinals together with $\omega_1$. The point $\omega_1$ is known to be a $C^*$-point as well as a $P$-point. We supply a characterization of $C^*$-points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a $C^*$-point. This process leads to many interesting new discoveries. (English) |
| Keyword: | ring of continuous functions |
| Keyword: | $C^*$-embedded |
| Keyword: | $P$-point |
| MSC: | 54D15 |
| MSC: | 54F05 |
| MSC: | 54G10 |
| idZBL: | Zbl 07613033 |
| idMR: | MR4506135 |
| DOI: | 10.14712/1213-7243.2022.015 |
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| Date available: | 2022-11-02T09:20:43Z |
| Last updated: | 2023-03-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151088 |
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