Characterizations of Some Classes of Perfect Spaces in Terms of Continuous Selections Avoiding Supporting Sets

Volume 56 / 2008

Takamitsu Yamauchi Bulletin Polish Acad. Sci. Math. 56 (2008), 149-161 MSC: 54C60, 54C65, 54D15. DOI: 10.4064/ba56-2-6

Abstract

Some kinds of perfect spaces, including paracompact perfectly normal spaces and collectionwise normal perfect spaces, are characterized in terms of continuous selections avoiding supporting sets. A necessary and sufficient condition on a domain space for a selection theorem of E. Michael [Fund. Math. 47 (1959), 173–178] to hold is also obtained.

Authors

  • Takamitsu YamauchiDepartment of Mathematics
    Shimane University
    Matsue, 690-8504, Japan
    and
    Department of General Education
    Kure College of Technology
    Kure, 737-8506, Japan
    e-mail

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