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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On generalizations of Lavrentieff's theorem for Polish group actions

Authors: Longyun Ding and Su Gao
Journal: Trans. Amer. Math. Soc. 359 (2007), 417-426
MSC (2000): Primary 54H05, 22F05
Published electronically: August 24, 2006
MathSciNet review: 2247897
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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

Longyun Ding
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

Su Gao
Affiliation: Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, Texas 76210

PII: S 0002-9947(06)03991-2
Received by editor(s): December 13, 2004
Published electronically: August 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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