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Sets with the Baire property in topologies formed from a given topology and ideals of sets
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2017 (English)In: Questions and answers in General Topology, ISSN 0918-4732, Vol. 35, no 1, 59-76 p.Article in journal (Refereed) Published
Abstract [en]

Let X be a set, τ1, τ2 topologies on X and Bp(X, τi) the family of all subsets of X possessing the Baire property in (X, τi), i = 1, 2. In this paper we study conditions on τ1 and τ2 that imply a relationship (for example, inclusion or equality) between the families Bp(X, τ1) and Bp(X, τ2). We are mostly interested in the case where the topology τ2 is formed with the help of a local function defined by the topology τ1 and an ideal of sets I on X. We also consider several applications of the local function defined by the usual topology on the reals and the ideal of all meager sets there, for proving some known facts.

Place, publisher, year, edition, pages
Osaka: Symposium of General Topology / Iso Shinpojumu , 2017. Vol. 35, no 1, 59-76 p.
Keyword [en]
Baire property, π-compatible topologies, Admissible extension, Local function, ∗-topology, Vitali set and Bernstein set
National Category
Geometry Mathematical Analysis Algebra and Logic Probability Theory and Statistics Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-137546OAI: oai:DiVA.org:liu-137546DiVA: diva2:1097089
Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2017-05-22Bibliographically approved

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