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

Takamitsu Yamauchi (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Characterizations of z -Lindelöf spaces

Ahmad Al-Omari, Takashi Noiri (2017)

Archivum Mathematicum

A topological space ( X , τ ) is said to be z -Lindelöf  [1] if every cover of X by cozero sets of ( X , τ ) admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of z -Lindelöf spaces.

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