Linear $\sigma$-additivity and some applications
General Topology
2018-04-06 v3 Logic
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.
Keywords
Cite
@article{arxiv.0906.5136,
title = {Linear $\sigma$-additivity and some applications},
author = {Tal Orenshtein and Boaz Tsaban},
journal= {arXiv preprint arXiv:0906.5136},
year = {2018}
}