{
  "id": "1904.08969",
  "version": "v1",
  "published": "2019-04-18T18:30:11.000Z",
  "updated": "2019-04-18T18:30:11.000Z",
  "title": "$k$-Scattered spaces",
  "authors": [
    "Taras Banakh"
  ],
  "comment": "4 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "A topological space $X$ is called $k$-scattered if each compact subspace of $X$ has an isolated point. We prove that (i) a \\v{C}ech-complete space is $k$-scattered if and only if it is scattered and (ii) a $K$-analytic space $X$ is $k$-scattered if and only if any metrizable continuous image of $X$ is at most countable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-18T18:30:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H05",
      "03E15",
      "03E17"
    ],
    "keywords": [
      "scattered spaces",
      "compact subspace",
      "analytic space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}