Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
$\sigma$-$(P)$-property; $cn$-network; $ck$-network; strict $\sigma$-space; strict $\aleph$-space
$\sigma$-$(P)$-property; $cn$-network; $ck$-network; strict $\sigma$-space; strict $\aleph$-space
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 $\mathcal F_n(X)$.
References:
[1] Borsuk K., Ulam S.: On symmetric products of topological spaces. Bull. Amer. Math. Soc. 37 (1931), no. 12, 875–882. DOI 10.1090/S0002-9904-1931-05290-3 | MR 1562283 | Zbl 0003.22402
[2] Gabriyelyan S. S., Kakol J.: On $\mathfrak{P}$-spaces and related concepts. Topology Appl. 191 (2015), 178–198. MR 3361065
[3] Good C., Macías S.: Symmetric products of generalized metric spaces. Topology Appl. 206 (2016), 93–114. MR 3494434
[4] Peng L.-X., Sun Y.: A study on symmetric products of generalized metric spaces. Topology Appl. 231 (2017), 411–429. DOI 10.1016/j.topol.2017.09.036 | MR 3712980
[5] Tang Z., Lin S., Lin F.: Symmetric products and closed finite-to-one mappings. Topology Appl. 234 (2018), 26–45. DOI 10.1016/j.topol.2017.11.004 | MR 3739454
Search
Partner of
