| Title:
|
On some classes of spaces with the $D$-property (English) |
| Author:
|
Martínez, Juan Carlos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
247-256 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall prove that under CH every regular meta-Lindelöf $P$-space which is locally $D$ has the $D$-property. In addition, we shall prove that a regular submeta-Lindelöf $P$-space is $D$ if it is locally $D$ and has locally extent at most $\omega_1$. Moreover, these results can be extended from the class of locally $D$-spaces to the wider class of $\mathbb D$-scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology Appl. 157 (2010), 378--384] which states that every weak $\overline{\theta}$-refinable $\mathbb D$-scattered space is $D$. (English) |
| Keyword:
|
property $D$ |
| Keyword:
|
meta-Lindelöf |
| Keyword:
|
weak $\overline{\theta}$-refinable |
| Keyword:
|
$P$-space |
| Keyword:
|
scattered space |
| MSC:
|
54A35 |
| MSC:
|
54D20 |
| MSC:
|
54G10 |
| idZBL:
|
Zbl 06391541 |
| idMR:
|
MR3193929 |
| . |
| Date available:
|
2014-06-07T15:41:13Z |
| Last updated:
|
2016-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143805 |
| . |
| Reference:
|
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| Reference:
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| . |
