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On the families of sets without the Baire property generated by the Vitali sets
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Department of MathematicsNational University of RwandaButareRwanda.
2011 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 3, no 2, 100-107 p.Article in journal (Refereed) Published
Abstract [en]

Let A be the family of all meager sets of the real line ℝ, V be the family of all Vitali sets of ℝ, V1be the family of all finite unions of elements of V and V2 = {(C \ A1) ∪ A2: C ∈ V1; A1, A2 ∈ A}. We show that the families VV1, V2 are invariant under translations of ℝ, and V1, V2 are abelian semigroups with the respect to the operation of union of sets. Moreover, V ⊂ V1 ⊂ V2 and V2consists of zero-dimensional sets without the Baire property. Then we extend the results above to the Euclidean spaces ℝnn ≥ 2, and their products with the finite powers of the Sorgenfrey line.

Place, publisher, year, edition, pages
Springer, 2011. Vol. 3, no 2, 100-107 p.
Keyword [en]
Vitali set of ℝn, Baire property, nonmeasurable set in the sense of Lebesgue, Sorgenfrey line
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-136258DOI: 10.1134/S2070046611020026OAI: oai:DiVA.org:liu-136258DiVA: diva2:1086505
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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