Haar meager sets, their hulls, and relationship to compact sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Dolezal, Martin¹  Vlasak, Vaclav² 

[1] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567 1, Czech Republic

[2] Charles Univ Prague, Fac Math & Phys, Ke Karlovu 8, Prague 12116 2, Czech Republic

关键词: Polish groups;    Haar null;    Haar meager;   

DOI  :  10.1016/j.jmaa.2016.09.017

来源: Elsevier

【 摘 要 】

Let G be an abelian Polish group. We show that there is a strongly Haar meager set in G without any F-sigma. Haar meager hull (and that this still remains true if we replace F-sigma by any other class of the Borel hierarchy). We also prove that there is a coanalytic naively strongly Haar meager set without any Haar meager hull. Further, we investigate the relationship of the collection of all compact sets to the collection of all Haar meager sets in non-locally compact Polish groups. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free