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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
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Category: math
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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
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Date available: 2020-10-13T13:15:53Z
Last updated: 2021-02-25
Stable URL: http://hdl.handle.net/10338.dmlcz/148281
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