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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Linear $\sigma$-additivity and some applications
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by Tal Orenshtein and Boaz Tsaban PDF
Trans. Amer. Math. Soc. 363 (2011), 3621-3637 Request permission


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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Additional Information
  • Tal Orenshtein
  • Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
  • Email:
  • Boaz Tsaban
  • Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
  • MR Author ID: 632515
  • Email:
  • Received by editor(s): August 2, 2009
  • Received by editor(s) in revised form: October 20, 2009
  • Published electronically: February 7, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3621-3637
  • MSC (2010): Primary 54D20, 54D80, 54H11; Secondary 03E17, 03E35
  • DOI:
  • MathSciNet review: 2775821