The Vietoris hyperspace $\mathcal F(X)$ and certain generalized metric properties

Year 2024, Volume: 53 Issue: 2, 356 - 366, 23.04.2024

Luong Quoc Tuyen , Tuyen Ong Van , Ljubiša D. R. Kočinac

https://doi.org/10.15672/hujms.1203236

Abstract

In this paper, we study several generalized metric properties of the space $\mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. In particular, we consider such properties $(P)$ for which $\mathcal F(X)$ has $(P)$ if and only if $X$ has $(P)$. Also, we obtain some results related to the images of metric spaces under some kinds of continuous mappings.

Keywords

hyperspace, generalized metric properties, $cs$-cover, $cs^*$-cover, $sn$-symmetric space, (weak) Cauchy symmetric space, (weak) Cauchy $sn$-symmetric space

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