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Products of Borel subgroups
Author(s):
Longyun
Ding;
Bingqing
Li
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3319-3326.
MSC (2000):
Primary 03E15, 54H05, 22A05
Posted:
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  subgroups whose product is not Borel in every uncountable abelian Polish group.
References:
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- 2.
- L. Ding and S. Gao, Diagonal actions and Borel equivalence relations, J. Symbolic Logic 71 (2006), no. 4, 1081-1096. MR 2275849 (2007h:03094)
- 3.
- L. Ding and S. Gao, Graev metric groups and Polishable subgroups, Adv. Math. 213 (2007), no. 2, 887-901.MR 2332614
- 4.
- A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, Berlin, 1995. MR 1321597 (96e:03057)
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- R.D. Mauldin, On the Borel subspaces of algebraic structures, Indiana Univ. Math. J. 29 (1980), no. 2, 261-265. MR 563210 (81i:54027)
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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:
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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