| Title:
|
Addition theorems and $D$-spaces (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Buzyakova, R. Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
653-663 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that if a regular space $X$ is the union of a finite family of metrizable subspaces then $X$ is a $D$-space in the sense of E. van Douwen. It follows that if a regular space $X$ of countable extent is the union of a finite collection of metrizable subspaces then $X$ is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a $D$-space. Some other new results on the properties of spaces which are unions of a finite collection of nice subspaces are obtained. (English) |
| Keyword:
|
$D$-space |
| Keyword:
|
point-countable base |
| Keyword:
|
extent |
| Keyword:
|
metrizable space |
| Keyword:
|
Lindelöf space |
| MSC:
|
54D20 |
| MSC:
|
54E35 |
| MSC:
|
54F99 |
| idZBL:
|
Zbl 1090.54017 |
| idMR:
|
MR2045787 |
| . |
| Date available:
|
2009-01-08T19:25:55Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119354 |
| . |
| Reference:
|
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| Reference:
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| . |
