A+ CATEGORY SCIENTIFIC UNIT

Open maps having the Bula property

Volume 205 / 2009

Valentin Gutev, Vesko Valov Fundamenta Mathematicae 205 (2009), 91-104 MSC: Primary 54F45, 54F35, 54C60, 54C65; Secondary 55M10, 54C35, 54B20. DOI: 10.4064/fm205-2-1

Abstract

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.

Authors

  • Valentin GutevSchool of Mathematical Sciences
    University of KwaZulu-Natal
    Westville Campus
    Private Bag X54001
    Durban 4000, South Africa
    e-mail
  • Vesko ValovDepartment of Computer Science and Mathematics
    Nipissing University
    100 College Drive
    P.O. Box 5002
    North Bay, ON
    P1B 8L7, Canada
    e-mail

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