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 : 128 | Download : 261

Publication Date : 2024-04-23

Article Type : Research Paper

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