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Non-meagre subgroups of reals disjoint with meagre sets
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SYSNO ASEP 0488977 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Non-meagre subgroups of reals disjoint with meagre sets Author(s) Kostana, Ziemowit (MU-W) SAI, RID Source Title Topology and its Applications. - : Elsevier - ISSN 0166-8641
Roč. 241, June (2018), s. 11-19Number of pages 9 s. Language eng - English Country NL - Netherlands Keywords algebraic sum ; Baire property ; non-meaurable subgroup Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 UT WOS 000432506300002 EID SCOPUS 85044575839 DOI 10.1016/j.topol.2018.03.019 Annotation 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]. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2019
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