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.
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