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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-1,
author = {Valentin Gutev and Vesko Valov},
title = {Open maps having the Bula property},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {91-104},
zbl = {1192.54015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-1}
}
Valentin Gutev; Vesko Valov. Open maps having the Bula property. Fundamenta Mathematicae, Tome 205 (2009) pp. 91-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-1/