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On countable unions of nonmeager sets in hereditarily Lindelöf spaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2011 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 3, no 1, 1-6 p.Article in journal (Refereed) Published
Abstract [en]

t is well known that any Vitali set on the real line ℝ does not possess the Baire property. The same is valid for finite unions of Vitali sets. What can be said about infinite unions of Vitali sets? Let S be a Vitali set, Sr be the image of S under the translation of ℝ by a rational number r and F = {Srr is rational}. We prove that for each non-empty proper subfamily F′ of F the union ∪F′ does not possess the Baire property. We say that a subset A of ℝ possesses Vitali property if there exist a non-empty open set O and a meager set M such that A ⊃ O \ M. Then we characterize those non-empty proper subfamilies F′ of F which unions ∪F′ possess the Vitali property.

Place, publisher, year, edition, pages
Springer, 2011. Vol. 3, no 1, 1-6 p.
Keyword [en]
Vitali set, Baire property, Vitali property
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-136259DOI: 10.1134/S2070046611010018OAI: oai:DiVA.org:liu-136259DiVA: diva2:1086500
Available from: 2017-04-03 Created: 2017-04-03 Last updated: 2017-04-12Bibliographically approved

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Chatyrko, Vitalij A.
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