Linear 𝜎-additivity and some applications

Orenshtein, Tal; Tsaban, Boaz

doi:10.1090/S0002-9947-2011-05228-1

Linear $\sigma$-additivity and some applications
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by Tal Orenshtein and Boaz Tsaban

Trans. Amer. Math. Soc. 363 (2011), 3621-3637

DOI: https://doi.org/10.1090/S0002-9947-2011-05228-1

Published electronically: February 7, 2011

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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 (1996), Gruenhage and Szeptycki (2005), Tsaban and Zdomskyy (2008), and Tsaban (2006), (2007), and construct topological groups with very strong combinatorial properties.

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