Some Results on the Countable Compactness and Pseudocompactness of Hyperspaces

Abstract

Let X be a Hausdorff space. Let 2 X denote the set of all non-empty closed subsets of X. For a subset A of X, we set 2 A = { F 6 2X : F ⊆ A }. Recall that the finite topology on 2 X is that topology having as a sub-basis the family { 2 G : G is open in X } U } 2 X — 2 F : F is closed in X). When endowed with this topology, 2 X is referred to as the hyper space of X. For the fundamental properties of hyperspaces, we refer the reader to [6; 7]. Following [6], we adopt the following notation: If A 0 , A 1 , … , A n are subsets of X, we set and for all .

Locations

• Canadian Journal of Mathematics - View - PDF