{
  "id": "1601.08168",
  "version": "v1",
  "published": "2016-01-29T16:04:53.000Z",
  "updated": "2016-01-29T16:04:53.000Z",
  "title": "Lower-Vietoris-type Topologies on Hyperspaces",
  "authors": [
    "Elza Ivanova-Dimova"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We introduce a new lower-Vietoris-type hypertopology in a way similar to that with which a new upper-Vietoris-type hypertopology was introduced in G. Dimov and D. Vakarelov, \"On Scott consequence systems\", Fundamenta Informaticae, 33 (1998), 43-70. (it was called there {\\em Tychonoff-type hypertopology}). We study this new hypertopology and, in particular, we generalize many results from E. Cuchillo-Ibanez, M. A. Moron and F. R. Ruiz del Portal, \"Lower semifinite topology in hyperspaces\", Topology Proceedings, 17 (1992), 29-39. As a corollary, we get that for every continuous map $f:X\\longrightarrow X$, where $X$ is a continuum, there exist a subcontinuum $K$ of $X$ such that $f(K)=K.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-29T16:04:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54H25",
      "54F15",
      "54C05"
    ],
    "keywords": [
      "lower-vietoris-type topologies",
      "hyperspaces",
      "scott consequence systems",
      "ruiz del portal",
      "lower semifinite topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160108168I"
    }
  }
}