1School of Mathematical Sciences University of KwaZulu-Natal Westville Campus Private Bag X54001 Durban 4000, South Africa 2Department of Computer Science and Mathematics Nipissing University 100 College Drive P.O. Box 5002 North Bay, ON P1B 8L7, Canada
Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 91-104
An open continuous map $f$ from a space $X$ onto a paracompact $C$-space $Y$ admits two disjoint closed sets $F_0,F_1\subset X$ with $f(F_0)=Y=f(F_1)$, 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.
Keywords:
continuous map space paracompact c space admits disjoint closed sets subset provided fibers infinite * embedded applications given existence disjoint usco multiselections set valued mappings defined paracompact c spaces special type factorizations continuous maps metrizable spaces paracompact c spaces settles several questions
Affiliations des auteurs :
Valentin Gutev
1
;
Vesko Valov
2
1
School of Mathematical Sciences University of KwaZulu-Natal Westville Campus Private Bag X54001 Durban 4000, South Africa
2
Department of Computer Science and Mathematics Nipissing University 100 College Drive P.O. Box 5002 North Bay, ON P1B 8L7, Canada
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author = {Valentin Gutev and Vesko Valov},
title = {Open maps having the {Bula} property},
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Valentin Gutev; Vesko Valov. Open maps having the Bula property. Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 91-104. doi: 10.4064/fm205-2-1
