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ISSN 1088-6850(e) ISSN 0002-9947(p)

Analytic groups and pushing small sets apart

Author(s): Jan van Mill
Journal: Trans. Amer. Math. Soc. 361 (2009), 5417-5434.
MSC (2000): Primary 54H05, 54E52, 03E15
Posted: May 12, 2009
MathSciNet review: 2515817
Retrieve article in: PDF

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Abstract: We say that a space has the separation property provided that if and are subsets of with countable and first category, then there is a homeomorphism $f\colon X\to X$ such that $f(A)\cap B=\emptyset$ . 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 come from the homeomorphisms given by an action of an analytic group, then is Polish. Several examples are also presented.

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