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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 $\tau$.

References [Enhancements On Off] (What's this?)

  • 1. H. Becker and A.S. Kechris, The descriptive set theory of Polish group actions, to appear in the London Mathematical Society Lecture Notes Series, 232, 1996. CMP 97:06
  • 2. E. Hewitt and K.A. Ross, Abstract harmonic analysis, Vol. I, Springer-Verlag, Berlin and New-York, 1979. MR 81k:43001
  • 3. A.S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics Series, Springer-Verlag, Berlin and New-York, 1995. MR 96e:03057
  • 4. M.G. Megrelishvili, A Tikhonov $G$-space that does not have compact $G$-extension and $G$-linearization, Uspekhi Matematicheskikh Nauk, vol. 43(1988), pp. 145-6. MR 89e:54080
  • 5. R. Sami, Polish group actions and the topological Vaught conjecture, Transactions of the American Mathematical Society, vol. 341(1994), pp. 335-353. MR 94c:03068
  • 6. R. Vaught, A Borel invariantization, Bulletin of the American Mathematical Society, vol. 79(1973), pp. 1291-5. MR 48:10818
  • 7. R. Vaught, Invariant sets in topology and logic, Fundamenta Mathematica, vol. 82(1974), pp. 269-94.MR 51:167

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Additional Information

Greg Hjorth
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555

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

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