Hyperspace of the Π-Complete Spaces and Maps

Abstract

In the present paper we establish that the space expβ X of compact subsets of a Tychonoff space X is Π-complete if and only if X is so. Further, we prove the Tychonoff map expβ f : expβ X → expβ Y is Π-complete if and only if a given map f : X → Y is Π-complete.