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 language | English |
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Pages (from-to) | 5417-5434 |
Number of pages | 18 |
Journal | Transactions of the American Mathematical Society |
Volume | 361 |
DOIs | |
Publication status | Published - 2009 |