On Martin's axiom and perfect spaces

Teodor C. Przymusiński

Displaying similar documents to “On Martin's axiom and perfect spaces”

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

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Bulletin of the Polish Academy of Sciences. Mathematics

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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.

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We prove that if there exists a Cohen real over a model, then the family of perfect sets coded in the model has a disjoint refinement by perfect sets.