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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Linear $ \sigma$-additivity and some applications


Authors: Tal Orenshtein and Boaz Tsaban
Journal: Trans. Amer. Math. Soc. 363 (2011), 3621-3637
MSC (2010): Primary 54D20, 54D80, 54H11; Secondary 03E17, 03E35
Published electronically: February 7, 2011
MathSciNet review: 2775821
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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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Additional Information

Tal Orenshtein
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Email: talo@weizmann.ac.il

Boaz Tsaban
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: tsaban@math.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05228-1
PII: S 0002-9947(2011)05228-1
Received by editor(s): August 2, 2009
Received by editor(s) in revised form: October 20, 2009
Published electronically: February 7, 2011
Article copyright: © Copyright 2011 American Mathematical Society