{
  "id": "1801.05633",
  "version": "v1",
  "published": "2018-01-17T12:09:54.000Z",
  "updated": "2018-01-17T12:09:54.000Z",
  "title": "The Baire category of the hyperspace of nontrivial convergent sequences",
  "authors": [
    "Michał Popławski"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Assume that $X$ is a regular space. We study topological properties of the family $S_c(X)$ of nontrivial convergent sequences in $X$ equipped with the Vietoris topology. We show that if $X$ has no isolated points, then $S_c(X)$ is a space of the first category which answers the question posed by S. Garcia-Ferreira and Y.F. Ortiz-Castillo.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-17T12:09:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54E52",
      "54A20"
    ],
    "keywords": [
      "nontrivial convergent sequences",
      "baire category",
      "hyperspace",
      "regular space",
      "study topological properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}