{
  "id": "1911.12940",
  "version": "v1",
  "published": "2019-11-29T03:38:20.000Z",
  "updated": "2019-11-29T03:38:20.000Z",
  "title": "Some generalized metric properties on hyperspaces with the Vietoris topology",
  "authors": [
    "Fucai Lin",
    "Rongxin Shen",
    "Chuan Liu"
  ],
  "comment": "18",
  "categories": [
    "math.GN"
  ],
  "abstract": "We study the heredity of the classes of generalized metric spaces (for example, spaces with a $\\sigma$-hereditarily closure-preserving $k$-network, spaces with a point-countable base, spaces with a base of countable order, spaces with a point-regular base, Nagata-spaces, $c$-semi-stratifiable spaces, $\\gamma$-spaces, semi-metrizable spaces) to the hyperspaces of nonempty compact subsets and finite subsets with the Vietoris topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-29T03:38:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54D20"
    ],
    "keywords": [
      "generalized metric properties",
      "vietoris topology",
      "hyperspaces",
      "nonempty compact subsets",
      "generalized metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}