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Linear $\sigma$-additivity and some applications

By Tal Orenshtein and Boaz Tsaban

Abstract

We show that countable increasing unions preserve a large family of well-studied covering properties, which are not necessarily sigma-additive. Using this, together with infinite-combinatorial methods and simple forcing theoretic methods, we explain several phenomena, settle problems of Just, Miller, Scheepers and Szeptycki [COC2], Gruenhage and Szeptycki [FUfin], Tsaban and Zdomskyy [SFT], and Tsaban [o-bdd, OPiT], and construct topological groups with very strong combinatorial properties

Topics: Mathematics - General Topology, Mathematics - Logic
Publisher: 'American Mathematical Society (AMS)'
Year: 2010
DOI identifier: 10.1090/S0002-9947-2011-05228-1
OAI identifier: oai:arXiv.org:0906.5136

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