Open maps having the Bula property

Abstract

Abstract. An open continuous map f from a space X onto a paracompact C-space Y admits two disjoint closed sets F0, F1 ⊂ X with f (F0) = Y = f (F1), provided all fibers of f are infinite and C * -embedded in X. Applications are given to the existence of "disjoint" usco multiselections of set-valued l.s.c. mappings defined on paracompact C-spaces, and to special type of factorizations of open continuous maps from metrizable spaces onto paracompact C-spaces. This settles several open questions.