{
  "id": "1611.06438",
  "version": "v1",
  "published": "2016-11-19T22:34:35.000Z",
  "updated": "2016-11-19T22:34:35.000Z",
  "title": "$ω^ω$-Dominated function spaces and $ω^ω$-bases in free objects of Topological Algebra",
  "authors": [
    "Taras Banakh",
    "Arkady Leiderman"
  ],
  "comment": "30 pages. arXiv admin note: text overlap with arXiv:1606.01967",
  "categories": [
    "math.GN",
    "math.FA",
    "math.GR"
  ],
  "abstract": "A topological space $X$ is defined to have an $\\omega^\\omega$-base} if at each point $x\\in X$ the space $X$ has a neighborhood base $(U_\\alpha[x])_{\\alpha\\in\\omega^\\omega}$ such that $U_\\beta[x]\\subset U_\\alpha[x]$ for all $\\alpha\\le\\beta$ in $\\omega^\\omega$. We characterize topological and uniform spaces whose free (locally convex) topological vector spaces or free (Abelian or Boolean) topological groups have $\\omega^\\omega$-bases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-19T22:34:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D70",
      "06A06",
      "08B20",
      "54H11",
      "22A99",
      "46A99"
    ],
    "keywords": [
      "dominated function spaces",
      "free objects",
      "topological algebra",
      "neighborhood base",
      "uniform spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}