{
  "id": "2303.11768",
  "version": "v1",
  "published": "2023-03-21T11:39:11.000Z",
  "updated": "2023-03-21T11:39:11.000Z",
  "title": "The Hurewicz Property and the Vietoris Hyperspace",
  "authors": [
    "Christopher Caruvana"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this note, we characterize when the Vietoris space of compact subsets of a given space has the Hurewicz property in terms of a selection principle on the given space itself using $k$-covers and the notion of groupability introduced by Ko\\v{c}inac and Scheepers. Using similar techniques, we also establish another equivalent condition to a space being Hurewicz in each of its finite powers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-21T11:39:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "54B20"
    ],
    "keywords": [
      "hurewicz property",
      "vietoris hyperspace",
      "vietoris space",
      "selection principle",
      "equivalent condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}