- Hacettepe Journal of Mathematics and Statistics
- Cilt: 53 Sayı: 2
- The Vietoris hyperspace $\\mathcal F(X)$ and certain generalized metric properties
The Vietoris hyperspace $\\mathcal F(X)$ and certain generalized metric properties
Authors : Luong Quoc Tuyen, Tuyen Ong Van, Ljubiša D. R. Kočinac
Pages : 356-366
Doi:10.15672/hujms.1203236
View : 118 | Download : 257
Publication Date : 2024-04-23
Article Type : Research
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