Analytic groups and pushing small sets apart

J. van Mill

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Abstract

We say that a space X has the separation property provided that if A and B are subsets of X with A countable and B first category, then there is a homeomorphism f: X → X such that f(A) ∩ B = Ø. We prove that a Borel space with this property is Polish. Our main result is that if the homeomorphisms needed in the separation property for the space X come from the homeomorphisms given by an action of an analytic group, then X is Polish. Several examples are also presented. © 2009 American Mathematical Society.
Original languageEnglish
Pages (from-to)5417-5434
Number of pages18
JournalTransactions of the American Mathematical Society
Volume361
DOIs
Publication statusPublished - 2009

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