{
  "id": "1607.07978",
  "version": "v1",
  "published": "2016-07-27T06:43:06.000Z",
  "updated": "2016-07-27T06:43:06.000Z",
  "title": "$ω^ω$-bases in topological and uniform spaces",
  "authors": [
    "Taras Banakh"
  ],
  "comment": "40 pages",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "We study topological properties of topological spaces with a local $\\omega^\\omega$-base and uniform spaces with an $\\omega^\\omega$-base. A topological space $X$ is defined to have a local $\\omega^\\omega$-base if each point of $X$ has a neighborhood base $\\{U_\\alpha\\}_{\\alpha\\in\\omega^\\omega}$ such that $U_\\beta\\subset U_\\alpha$ for all $\\alpha\\le\\beta$ in $\\omega^\\omega$. A uniform space $X$ is defined to have an $\\omega^\\omega$-base if it has a base $\\{U_\\alpha\\}_{\\alpha\\in\\omega^\\omega}$ of the uniformity such that $U_\\beta\\subset U_\\alpha$ for all $\\alpha\\le\\beta$ in $\\omega^\\omega$. Our results show that topological spaces with a local $\\omega^\\omega$-base and uniform spaces with an $\\omega^\\omega$-base possess many properties, typical for generalized metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-27T06:43:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D70",
      "54E15",
      "54E18",
      "54E35",
      "03E04",
      "03E17",
      "54A20",
      "54A25",
      "54A35",
      "54C35",
      "54D15",
      "54D45",
      "54D65",
      "54D70",
      "54G10",
      "54G20"
    ],
    "keywords": [
      "uniform space",
      "topological space",
      "generalized metric spaces",
      "study topological properties",
      "base possess"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}