Transactions of the American Mathematical Society

Author(s): Jan van Mill
Journal: Trans. Amer. Math. Soc. 361 (2009), 5417-5434.
MSC (2000): Primary 54H05, 54E52, 03E15
Posted: May 12, 2009
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 54H05, 54E52, 03E15

Jan van Mill
Affiliation: Faculty of Sciences, Department of Mathematics, VU University Amsterdam, De Boelelaan 1081${}^a$, 1081 HV Amsterdam, The Netherlands
Email: vanmill@few.vu.nl

DOI: 10.1090/S0002-9947-09-04665-0
PII: S 0002-9947(09)04665-0
Keywords: Analytic group, meager set, countable set, Polish space.
Received by editor(s): May 29, 2007
Received by editor(s) in revised form: October 18, 2007
Posted: May 12, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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