| Title:
|
Addition theorems for dense subspaces (English) |
| Author:
|
Arhangel'skii, A. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
531-541 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study topological spaces that can be represented as the union of a finite collection of dense metrizable subspaces. The assumption that the subspaces are dense in the union plays a crucial role below. In particular, Example 3.1 shows that a paracompact space $X$ which is the union of two dense metrizable subspaces need not be a $p$-space. However, if a normal space $X$ is the union of a finite family $\mu $ of dense subspaces each of which is metrizable by a complete metric, then $X$ is also metrizable by a complete metric (Theorem 2.6). We also answer a question of M.V. Matveev by proving in the last section that if a Lindelöf space $X$ is the union of a finite family $\mu $ of dense metrizable subspaces, then $X$ is separable and metrizable. (English) |
| Keyword:
|
dense subspace |
| Keyword:
|
perfect space |
| Keyword:
|
Moore space |
| Keyword:
|
Čech-complete |
| Keyword:
|
$p$-space |
| Keyword:
|
$\sigma $-disjoint base |
| Keyword:
|
uniform base |
| Keyword:
|
pseudocompact |
| Keyword:
|
point-countable base |
| Keyword:
|
pseudo-$\omega _1$-compact |
| MSC:
|
54A25 |
| MSC:
|
54B05 |
| idZBL:
|
Zbl 06537722 |
| idMR:
|
MR3434227 |
| DOI:
|
10.14712/1213-7243.2015.142 |
| . |
| Date available:
|
2015-12-17T11:52:47Z |
| Last updated:
|
2018-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144757 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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