Geodesic
Open maps having the Bula property
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
Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 91-104 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm205-2-1
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

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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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

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