{
  "id": "0906.5136",
  "version": "v3",
  "published": "2009-06-28T13:40:21.000Z",
  "updated": "2010-11-04T19:44:30.000Z",
  "title": "Linear $σ$-additivity and some applications",
  "authors": [
    "Tal Orenshtein",
    "Boaz Tsaban"
  ],
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-04T19:44:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "applications",
      "additivity",
      "strong combinatorial properties",
      "simple forcing theoretic methods",
      "construct topological groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.5136O"
    }
  }
}