{
  "id": "1608.03043",
  "version": "v1",
  "published": "2016-08-10T04:39:34.000Z",
  "updated": "2016-08-10T04:39:34.000Z",
  "title": "Oscillation Revisited",
  "authors": [
    "Gerald Beer",
    "Jiling Cao"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In previous work by Beer and Levi [8, 9], the authors studied the oscillation $\\Omega (f,A)$ of a function $f$ between metric spaces $\\langle X,d \\rangle$ and $\\langle Y,\\rho \\rangle$ at a nonempty subset $A$ of $X$, defined so that when $A =\\{x\\}$, we get $\\Omega (f,\\{x\\}) = \\omega (f,x)$, where $\\omega (f,x)$ denotes the classical notion of oscillation of $f$ at the point $x \\in X$. The main purpose of this article is to formulate a general joint continuity result for $(f,A) \\mapsto \\Omega (f,A)$ valid for continuous functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T04:39:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E40",
      "54B20",
      "26A15",
      "54E35",
      "54C35"
    ],
    "keywords": [
      "oscillation",
      "general joint continuity result",
      "main purpose",
      "metric spaces",
      "nonempty subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}