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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sharper changes in topologies


Author: Greg Hjorth
Journal: Proc. Amer. Math. Soc. 127 (1999), 271-278
MSC (1991): Primary 04A15
MathSciNet review: 1458878
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Abstract: Let $G$ be a Polish group, $\tau$ a Polish topology on a space $X$, $G$ acting continuously on $(X,\tau)$, with $B\subset X$ $G$-invariant and in the Borel algebra generated by $\tau$. Then there is a larger Polish topology $\tau^*\supset \tau$ on $X$ so that $B$ is open with respect to $\tau^*$, $G$ still acts continuously on $(X,\tau^*)$, and $\tau^*$ has a basis consisting of sets that are of the same Borel rank as $B$ relative to $\tau$.


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Additional Information

Greg Hjorth
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
Email: greg@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04498-6
PII: S 0002-9939(99)04498-6
Keywords: Polish group, topological group, topology
Received by editor(s): October 17, 1996
Received by editor(s) in revised form: May 13, 1997
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1999 American Mathematical Society