{
  "id": "2006.04783",
  "version": "v1",
  "published": "2020-06-08T17:56:05.000Z",
  "updated": "2020-06-08T17:56:05.000Z",
  "title": "Distinguishing endpoint sets from Erdős space",
  "authors": [
    "David S. Lipham"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "We show that the set of all escaping endpoints of the Julia set of $\\exp(z)-1$ is not homeomorphic to $\\mathbb Q \\times X$ for any space $X$. In particular, it is not homeomorphic to Erd\\H{o}s space $\\mathfrak E$. Our proof demonstrates that the complement of the escaping endpoint set in $\\mathbb C$ is path-connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-08T17:56:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "54F45"
    ],
    "keywords": [
      "distinguishing endpoint sets",
      "erdős space",
      "homeomorphic",
      "escaping endpoint set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}