TY - JOUR
T1 - Linear σ-additivity and some applications
AU - Orenshtein, Tal
AU - Tsaban, Boaz
PY - 2011/7
Y1 - 2011/7
N2 - We show that countable increasing unions preserve a large family of well-studied covering properties, which are not necessarily s-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 andZdomskyy (2008), and Tsaban (2006), (2007), and construct topological groups with very strong combinatorial properties.
AB - We show that countable increasing unions preserve a large family of well-studied covering properties, which are not necessarily s-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 andZdomskyy (2008), and Tsaban (2006), (2007), and construct topological groups with very strong combinatorial properties.
UR - http://www.scopus.com/inward/record.url?scp=79953016301&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2011-05228-1
DO - 10.1090/S0002-9947-2011-05228-1
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AN - SCOPUS:79953016301
SN - 0002-9947
VL - 363
SP - 3621
EP - 3637
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 7
ER -