{
  "id": "1204.2887",
  "version": "v1",
  "published": "2012-04-13T06:23:41.000Z",
  "updated": "2012-04-13T06:23:41.000Z",
  "title": "Knot points of typical continuous functions",
  "authors": [
    "David Preiss",
    "Shingo Saito"
  ],
  "comment": "24 pages",
  "journal": "Trans. Amer. Math. Soc. 366 (2014), 833-856",
  "doi": "10.1090/S0002-9947-2013-06100-4",
  "categories": [
    "math.CA",
    "math.LO"
  ],
  "abstract": "It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strongest possible sense except in a small set of points. In this paper, we completely characterise families S of sets of points for which most continuous functions have the property that such small set of points belongs to S. The proof uses a topological zero-one law and the Banach-Mazur game.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-13T06:23:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A27",
      "26A21",
      "28A05",
      "54H05"
    ],
    "keywords": [
      "typical continuous functions",
      "knot points",
      "small set",
      "characterise families",
      "dini derivatives"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2887P"
    }
  }
}