Products of Borel subgroups

Ding, Longyun; Li, Bingqing

doi:10.1090/S0002-9939-08-09334-9

Products of Borel subgroups
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by Longyun Ding and Bingqing Li PDF

Proc. Amer. Math. Soc. 136 (2008), 3319-3326 Request permission

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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