{
  "id": "math/0612307",
  "version": "v1",
  "published": "2006-12-12T09:58:05.000Z",
  "updated": "2006-12-12T09:58:05.000Z",
  "title": "Spaces of functions with countably many discontinuities",
  "authors": [
    "R Haydon",
    "A Molto",
    "J Orihuela"
  ],
  "categories": [
    "math.FA",
    "math.GN"
  ],
  "abstract": "Let $\\Gamma$ be a Polish space and let $K$ be a separable and pointwise compact set of real-valued functions on $\\Gamma$. It is shown that if each function in $K$ has only countably many discontinuities then $C(K)$ may be equipped with a $T_p$-lower semicontinuous and locally uniformly convex norm, equivalent to the supremum norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-12T09:58:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "54H05"
    ],
    "keywords": [
      "discontinuities",
      "pointwise compact set",
      "locally uniformly convex norm",
      "supremum norm",
      "real-valued functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12307H"
    }
  }
}