Non-meagre subgroups of reals disjoint with meagre sets

0488977 - MÚ 2019 RIV NL eng J - Journal Article
Kostana, Ziemowit
Non-meagre subgroups of reals disjoint with meagre sets.
Topology and its Applications. Roč. 241, June (2018), s. 11-19. ISSN 0166-8641. E-ISSN 1879-3207
Institutional support: RVO:67985840
Keywords : algebraic sum * Baire property * non-meaurable subgroup
OECD category: Pure mathematics
Impact factor: 0.416, year: 2018
https://www.sciencedirect.com/science/article/pii/S0166864118300567

Let (X,+) denote (R,+) or (2ω,+2). We prove that for any meagre set F⊆X there exists a subgroup G≤X without the Baire property, disjoint with some translation of F. We point out several consequences of this fact and indicate why analogous result for the measure cannot be established in ZFC. We extend proof techniques from [1].
Permanent Link: http://hdl.handle.net/11104/0283475