Geodesic
On the $n$-fold symmetric product of a space with a $\sigma$-$(P)$-property $cn$-network ($ck$-network)
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 257-263.

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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 $\mathcal F_n(X)$.
DOI : 10.14712/1213-7243.2020.025
Classification : 54B20, 54D20
Keywords: $\sigma$-$(P)$-property; $cn$-network; $ck$-network; strict $\sigma$-space; strict $\aleph$-space 
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Tuyen, Luong Q.; Tuyen, Ong V. On the $n$-fold symmetric product of a space with a $\sigma$-$(P)$-property $cn$-network ($ck$-network). Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 257-263. doi : 10.14712/1213-7243.2020.025. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.025/

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