{
  "id": "1508.07788",
  "version": "v1",
  "published": "2015-08-31T12:32:16.000Z",
  "updated": "2015-08-31T12:32:16.000Z",
  "title": "Topological structures of hyperspaces of finite sets in non-separable metrizable spaces",
  "authors": [
    "Katsuhisa Koshino"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1503.08575. text overlap with arXiv:1508.05557",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let ${\\rm Fin}(X)$ be the hyperspace consisting of non-empty finite subsets of a space $X$ endowed with the Vietoris topology. In this paper, we characterize a metrizable space $X$ whose hyperspace ${\\rm Fin}(X)$ is homeomorphic to the linear subspace spanned by the canonical orthonormal basis of a non-separable Hilbert space of density $< \\mathfrak{d}$, where $\\mathfrak{d}$ is the dominating number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-31T12:32:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54F65",
      "57N20"
    ],
    "keywords": [
      "non-separable metrizable spaces",
      "finite sets",
      "topological structures",
      "hyperspace",
      "non-empty finite subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807788K"
    }
  }
}