{
  "id": "1701.01181",
  "version": "v1",
  "published": "2017-01-04T23:34:54.000Z",
  "updated": "2017-01-04T23:34:54.000Z",
  "title": "Vietoris-type Topologies on Hyperspaces",
  "authors": [
    "Elza Ivanova-Dimova"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We introduce a new Vietoris-type hypertopology by means of the upper-Vietoris-type hypertopology defined by G. Dimov and D. Vakarelov [On Scott consequence systems, Fundamenta Informaticae, 33 (1998), 43-70] (it was called there {\\em Tychonoff-type hypertopology}) and the lower-Vietoris-type hypertopology introduced by E. Ivanova-Dimova [Lower-Vietoris-type topologies on hyperspaces, Topology Appl. (to appear)]. We study this new Vietoris-type hypertopology and show that it is, in general, different from the Vietoris topology. Also, some of the results of E. Michael [Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182] about hyperspaces with Vietoris topology are extended to analogous results for hyperspaces with Vietoris-type topology. We obtain as well some results about hyperspaces with Vietoris-type topology which concern some problems analogous to those regarded by H.-J. Schmidt [Hyperspaces of quotient and subspaces. I. Hausdorff topological spaces, Math. Nachr. 104 (1981), 271-280].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-04T23:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54D10",
      "54C05"
    ],
    "keywords": [
      "vietoris-type topology",
      "hyperspaces",
      "vietoris topology",
      "scott consequence systems",
      "hausdorff topological spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}