DOI: 10.15672/hujms.1203236 ISSN:

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

Ljubiša D. R. KOČİNAC, Luong Quoc TUYEN, Tuyen ONG VAN
  • Geometry and Topology
  • Statistics and Probability
  • Algebra and Number Theory
  • Analysis
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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.

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