{
  "id": "2010.13876",
  "version": "v1",
  "published": "2020-10-26T19:57:44.000Z",
  "updated": "2020-10-26T19:57:44.000Z",
  "title": "Another almost zero-dimensional space of exact multiplicative class 3",
  "authors": [
    "David S. Lipham"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GN",
    "math.CV"
  ],
  "abstract": "We show that the escaping set for $f(z)=\\exp(z)-1$ is nowhere $\\sigma$-complete. This establishes that the escaping endpoint set $\\dot E(f)$ is a first category almost zero-dimensional space which is $F_{\\sigma\\delta}$ and nowhere $G_{\\delta \\sigma}$. Only two other elementary spaces with those properties are known: $\\mathbb Q ^\\omega$ and Erd\\H{o}s space $\\mathfrak E$. Previous work has shown that $\\dot E(f)$ is homeomorphic to neither of those.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-26T19:57:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F45",
      "54H05",
      "30D05"
    ],
    "keywords": [
      "exact multiplicative class",
      "zero-dimensional space",
      "escaping endpoint set",
      "first category",
      "elementary spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}