| Title:
|
A generalization of Čech-complete spaces and Lindelöf $\Sigma $-spaces (English) |
| Author:
|
Arhangel'skii, A. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
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0010-2628 (print) |
| ISSN:
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1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
121-139 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The class of $s$-spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf $p$-spaces, metrizable spaces with the weight $\leq 2^\omega $, but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that $s$-spaces are in a duality with Lindelöf $\Sigma $-spaces: $X$ is an $s$-space if and only if some (every) remainder of $X$ in a compactification is a Lindelöf $\Sigma $-space [Arhangel'skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. {220} (2013), 71--81]. A basic fact is established: the weight and the networkweight coincide for all $s$-spaces. This theorem generalizes the similar statement about Čech-complete spaces. We also study hereditarily $s$-spaces, provide various sufficient conditions for a space to be a hereditarily $s$-space, and establish that every metrizable space has a dense subspace which is a hereditarily $s$-space. It is also shown that every dense-in-itself compact hereditarily $s$-space is metrizable. (English) |
| Keyword:
|
metrizable |
| Keyword:
|
Lindelöf $p$-space |
| Keyword:
|
Lindelöf $\Sigma $-space |
| Keyword:
|
remainder |
| Keyword:
|
compactification |
| Keyword:
|
$\sigma $-space |
| Keyword:
|
countable network |
| Keyword:
|
countable type |
| Keyword:
|
perfect mapping |
| MSC:
|
54A25 |
| MSC:
|
54B05 |
| idZBL:
|
Zbl 06221258 |
| idMR:
|
MR3067699 |
| . |
| Date available:
|
2013-06-25T12:45:55Z |
| Last updated:
|
2015-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143265 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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