| Title:
|
On the $n$-fold symmetric product of a space with a $\sigma$-$(P)$-property $cn$-network ($ck$-network) (English) |
| Author:
|
Tuyen, Luong Q. |
| Author:
|
Tuyen, Ong V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
257-263 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the relation between a space $X$ satisfying certain generalized metric properties and its $n$-fold symmetric product $\mathcal F_n(X)$ satisfying the same properties. We prove that $X$ has a $\sigma$-$(P)$-property $cn$-network if and only if so does $\,\mathcal F_n(X)$. Moreover, if $\,X$ is regular then $X$ has a $\sigma$-$(P)$-property $ck$-network if and only if so does $\,\mathcal F_n(X)$. By these results, we obtain that $X$ is strict $\sigma$-space (strict $\aleph$-space) if and only if so is $\mathcal F_n(X)$. (English) |
| Keyword:
|
$\sigma$-$(P)$-property |
| Keyword:
|
$cn$-network |
| Keyword:
|
$ck$-network |
| Keyword:
|
strict $\sigma$-space |
| Keyword:
|
strict $\aleph$-space |
| MSC:
|
54B20 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 07286004 |
| idMR:
|
MR4143708 |
| DOI:
|
10.14712/1213-7243.2020.025 |
| . |
| Date available:
|
2020-10-13T13:15:53Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148281 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Good C., Macías S.: Symmetric products of generalized metric spaces.Topology Appl. 206 (2016), 93–114. MR 3494434 |
| Reference:
|
[4] Peng L.-X., Sun Y.: A study on symmetric products of generalized metric spaces.Topology Appl. 231 (2017), 411–429. MR 3712980, 10.1016/j.topol.2017.09.036 |
| Reference:
|
[5] Tang Z., Lin S., Lin F.: Symmetric products and closed finite-to-one mappings.Topology Appl. 234 (2018), 26–45. MR 3739454, 10.1016/j.topol.2017.11.004 |
| . |
