| Title:
|
Spaces with large relative extent (English) |
| Author:
|
Song, Yan-Kui |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
387-394 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove the following statements: (1) For every regular uncountable cardinal $\kappa $, there exist a Tychonoff space $X$ and $Y$ a subspace of $X$ such that $Y$ is both relatively absolute star-Lindelöf and relative property (a) in $X$ and $e(Y,X) \ge \kappa $, but $Y$ is not strongly relative star-Lindelöf in $X$ and $X$ is not star-Lindelöf. (2) There exist a Tychonoff space $X$ and a subspace $Y$ of $X$ such that $Y$ is strongly relative star-Lindelöf in $X$ (hence, relative star-Lindelöf), but $Y$ is not absolutely relative star-Lindelöf in $X$. (English) |
| Keyword:
|
relative topological property |
| Keyword:
|
Lindelöf |
| Keyword:
|
star-Lindelöf |
| Keyword:
|
relative extent |
| Keyword:
|
relative property (a) |
| MSC:
|
54D15 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1174.54014 |
| idMR:
|
MR2309972 |
| . |
| Date available:
|
2009-09-24T11:46:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128178 |
| . |
| Reference:
|
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| Reference:
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| . |
