Sharper changes in topologies

Author:
Greg Hjorth

Journal:
Proc. Amer. Math. Soc. **127** (1999), 271-278

MSC (1991):
Primary 04A15

DOI:
https://doi.org/10.1090/S0002-9939-99-04498-6

MathSciNet review:
1458878

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Polish group, a Polish topology on a space , acting continuously on , with -invariant and in the Borel algebra generated by . Then there is a larger Polish topology on so that is open with respect to , still acts continuously on , *and* has a basis consisting of sets that are of the same Borel rank as relative to .

**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 -space that does not have compact -extension and -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

Email:
greg@math.ucla.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04498-6

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