Characterizations of Some Classes of Perfect Spaces in Terms of Continuous Selections Avoiding Supporting Sets
Volume 56 / 2008
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.
