THE σ-POINT-FINITE cn-NETWORKS (ck-NETWORKS) OF PIXLEY-ROY HYPERSPACES

Abstract

In this paper, we study the relation between a space $X$ satisfying certain generalized metric properties and the Pixley-Roy hyperspace $\mathcal{F}[X]$ over $X$ satisfying the same properties. We prove that if $X$ has a $\sigma$-point-finite $cn$-network (resp., $ck$-network), then $\mathcal{F}[X]$ also has a $\sigma$-point-finite $cn$-network (resp., $ck$-network).