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

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Hacettepe Journal of Mathematics and Statistics
Volume:53 Issue: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 : 136 | Download : 263

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

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