{
  "id": "2006.16946",
  "version": "v1",
  "published": "2020-06-30T16:40:14.000Z",
  "updated": "2020-06-30T16:40:14.000Z",
  "title": "Escaping sets are not sigma-compact",
  "authors": [
    "Lasse Rempe"
  ],
  "comment": "4 pages",
  "categories": [
    "math.DS",
    "math.CV",
    "math.GN"
  ],
  "abstract": "Let $f$ be a transcendental entire function. The escaping set $I(f)$ consists of those points that tend to infinity under iteration of $f$. We show that $I(f)$ is not $\\sigma$-compact, resolving a question of Rippon from 2009.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-30T16:40:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D05",
      "37F10",
      "54D45"
    ],
    "keywords": [
      "escaping set",
      "sigma-compact",
      "transcendental entire function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}