| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-11-02T09:20:43Z |
| Last updated:
|
2024-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151088 |
| . |
| Reference:
|
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| Reference:
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|
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| Reference:
|
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| . |
