On generalizations of Lavrentieff’s theorem for Polish group actions
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- by Longyun Ding and Su Gao PDF
- Trans. Amer. Math. Soc. 359 (2007), 417-426 Request permission
Abstract:
It is shown that for every Polish group $G$ that is not locally compact there is a continuous action $a$ of $G$ on a $\boldsymbol {\Pi }^1_1$-complete subset $A$ of a Polish space $X$ such that $a$ cannot be extended to any superset of $A$ in $X$. This answers a question posed by Becker and Kechris and shows that an earlier theorem of them is optimal in several aspects.References
- Howard Becker and Alexander S. Kechris, The descriptive set theory of Polish group actions, London Mathematical Society Lecture Note Series, vol. 232, Cambridge University Press, Cambridge, 1996. MR 1425877, DOI 10.1017/CBO9780511735264
- Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
- A. S. Kechris, A. Louveau, and W. H. Woodin, The structure of $\sigma$-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), no. 1, 263–288. MR 879573, DOI 10.1090/S0002-9947-1987-0879573-9
- M. Lavrentieff, Contribution à la théorie des ensembles homéomorphes, Fund. Math. 6 (1924), 149-160.
Additional Information
- Longyun Ding
- Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China
- Email: dingly@nankai.edu.cn
- Su Gao
- Affiliation: Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, Texas 76210
- MR Author ID: 347662
- Email: sgao@unt.edu
- Received by editor(s): December 13, 2004
- Published electronically: August 24, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 417-426
- MSC (2000): Primary 54H05, 22F05
- DOI: https://doi.org/10.1090/S0002-9947-06-03991-2
- MathSciNet review: 2247897