{
  "id": "1005.5542",
  "version": "v1",
  "published": "2010-05-30T15:40:30.000Z",
  "updated": "2010-05-30T15:40:30.000Z",
  "title": "Sequential properties of function spaces with the compact-open topology",
  "authors": [
    "Gary Gruenhage",
    "Boaz Tsaban",
    "Lyubomyr Zdomskyy"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let M be the countably infinite metric fan. We show that C_k(M,2) is sequential and contains a closed copy of Arens space S_2. It follows that if X is metrizable but not locally compact, then C_k(X) contains a closed copy of S_2, and hence does not have the property AP. We also show that, for any zero-dimensional Polish space X, C_k(X,2) is sequential if and only if X is either locally compact or the derived set X' is compact. In the case that X is a non-locally compact Polish space whose derived set is compact, we show that all spaces C_k(X, 2) are homeomorphic, having the topology determined by an increasing sequence of Cantor subspaces, the n-th one nowhere dense in the (n+1)-st.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-30T15:40:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function spaces",
      "compact-open topology",
      "sequential properties",
      "locally compact",
      "derived set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5542G"
    }
  }
}