Open maps having the Bula property

Details Open maps having the Bula property Open maps having the Bula property

2008-01-12

arxiv.org/abs/0801.1904v1

Mathematics

General Topology

16 pages

Scientific paper

Every open continuous map f from a space X onto a paracompact C-space Y admits two disjoint closed subsets of X so that their image by f is Y provided all fibers of f are infinite and C*-embedded in X. Applications are demonstrated for the existence of "disjoint" usco multiselections of set-valued l.s.c. mappings defined on paracompact C-spaces, and for special type of factorizations of open continuous maps from metrizable spaces onto paracompact C-spaces. This settles several open questions.

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