| Title:
|
A nice class extracted from $C_p$-theory (English) |
| Author:
|
Tkachuk, Vladimir V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
503-513 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, $\omega $-stable and $\omega $-monolithic. It is also established that any Sokolov compact space $X$ is Fréchet-Urysohn and the space $C_p(X)$ is Lindelöf. We prove that any Sokolov space with a $G_\delta $-diagonal has a countable network and obtain some cardinality restrictions on subsets of small pseudocharacter lying in $\Sigma $-products of cosmic spaces. (English) |
| Keyword:
|
Corson compact space |
| Keyword:
|
Sokolov space |
| Keyword:
|
extent |
| Keyword:
|
$\omega $-monolithic space |
| Keyword:
|
$\Sigma $-products |
| MSC:
|
54B10 |
| MSC:
|
54C05 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 1121.54019 |
| idMR:
|
MR2174528 |
| . |
| Date available:
|
2009-05-05T16:52:51Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119544 |
| . |
| Reference:
|
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| . |
