{
  "id": "math/0307225",
  "version": "v7",
  "published": "2003-07-16T15:18:13.000Z",
  "updated": "2010-10-31T20:05:46.000Z",
  "title": "o-bounded groups and other topological groups with strong combinatorial properties",
  "authors": [
    "Boaz Tsaban"
  ],
  "comment": "Small updates",
  "journal": "Proceedings of the American Mathematical Society 134 (2006), 881--891",
  "doi": "10.1090/S0002-9939-05-08034-2",
  "categories": [
    "math.GN",
    "math.CO",
    "math.GR",
    "math.LO"
  ],
  "abstract": "We construct several topological groups with very strong combinatorial properties. In particular, we give simple examples of subgroups of the real line R (thus strictly o-bounded) which have the Hurewicz property but are not sigma-compact, and show that the product of two o-bounded subgroups of R^N may fail to be o-bounded, even when they satisfy the stronger property S1(Borel_Omega,Borel_Omega). This solves a problem of Tkacenko and Hernandez, and extends independent solutions of Krawczyk and Michalewski and of Banakh, Nickolas, and Sanchis. We also construct separable metrizable groups G of size continuum such that every countable Borel omega-cover of G contains a gamma-cover of G.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2010-10-31T20:05:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "37F20"
    ],
    "keywords": [
      "strong combinatorial properties",
      "topological groups",
      "o-bounded groups",
      "extends independent solutions",
      "simple examples"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7225T"
    }
  }
}