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

 

Products of Borel subgroups


Authors: Longyun Ding and Bingqing Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 3319-3326
MSC (2000): Primary 03E15, 54H05, 22A05
Published electronically: April 29, 2008
MathSciNet review: 2407098
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Abstract: We investigate the Borelness of the product of two Borel subgroups in Polish groups. While the intersection of these two subgroups is Polishable, the Borelness of their product is confirmed. On the other hand, we construct two $ \boldsymbol{\Delta}^{0}_{3}$ subgroups whose product is not Borel in every uncountable abelian Polish group.


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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

Bingqing Li
Affiliation: Department of Risk Management and Insurance, Nankai University, Tianjin, 300071, People’s Republic of China
Email: bqlink@126.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09334-9
PII: S 0002-9939(08)09334-9
Keywords: Polish group, Borelness, Polishable subgroup
Received by editor(s): July 3, 2007
Published electronically: April 29, 2008
Additional Notes: The first author’s research was supported by the Science & Technology Innovation Fund of Nankai University Z1A2006015.
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.