Small-large subgroups of locally compact Abelian Polish groups

Abstract

In [arXiv:1605.02261] Rosłanowski and Shelah asked whether every locally compact non-discrete group has a null but non-meager subgroup, and conversely whether it is consistent with $ZFC$ that in every locally compact group there are no meager but non-null subgroups. The answer is affirmative for both questions [arXiv:1605.02261], however, in this paper we provide a much simpler proof for the special case of Abelian Polish groups.

arXiv commentarXiv admin note: text overlap with arXiv:1610.00614