{
  "id": "1511.07062",
  "version": "v1",
  "published": "2015-11-22T20:24:38.000Z",
  "updated": "2015-11-22T20:24:38.000Z",
  "title": "On topological groups admitting a base at identity indexed with ω^ω",
  "authors": [
    "Arkady G. Leiderman",
    "Vladimir G. Pestov",
    "Artur H. Tomita"
  ],
  "comment": "17 pages, latex 2e",
  "categories": [
    "math.GN"
  ],
  "abstract": "A topological group $G$ is said to have a $\\mathfrak G$-base if the neighbourhood system at identity admits a monotone cofinal map from the directed set $\\omega^\\omega$. In particular, every metrizable group is such, but the class of groups with a $\\mathfrak G$-base is significantly wider. The aim of this article is to better understand the boundaries of this class, by presenting new examples and counter-examples. Ultraproducts and non-arichimedean ordered fields lead to natural families of non-metrizable groups with a $\\mathfrak G$-base which nevertheless have the Baire property. More examples come from such constructions as the free topological group and the free Abelian topological group of a Tychonoff (more generally uniform) space, as well as the free product of topological groups. Our results answer some questions previously stated in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-22T20:24:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05"
    ],
    "keywords": [
      "topological groups admitting",
      "monotone cofinal map",
      "free abelian topological group",
      "results answer",
      "neighbourhood system"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151107062L"
    }
  }
}