{
  "id": "math/0606373",
  "version": "v3",
  "published": "2006-06-15T19:14:13.000Z",
  "updated": "2006-09-26T16:51:11.000Z",
  "title": "On metrizable enveloping semigroups",
  "authors": [
    "Eli Glasner",
    "Michael Megrelishvili",
    "Vladimir V. Uspenskij"
  ],
  "comment": "11 pages. Revised version 20 September 2006. Minor improvements",
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "When a topological group $G$ acts on a compact space $X$, its enveloping semigroup $E(X)$ is the closure of the set of $g$-translations, $g\\in G$, in the compact space $X^X$. Assume that $X$ is metrizable. It has recently been shown by the first two authors that the following conditions are equivalent: (1) $X$ is hereditarily almost equicontinuous; (2) $X$ is hereditarily non-sensitive; (3) for any compatible metric $d$ on $X$ the metric $d_G(x,y):=\\sup\\{d(gx,gy): g\\in G\\}$ defines a separable topology on $X$; (4) the dynamical system $(G,X)$ admits a proper representation on an Asplund Banach space. We prove that these conditions are also equivalent to the following: the enveloping semigroup $E(X)$ is metrizable.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-09-26T16:51:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H20",
      "22A25",
      "22F05",
      "37B05",
      "46B10",
      "46B22",
      "54H15"
    ],
    "keywords": [
      "metrizable enveloping semigroups",
      "compact space",
      "asplund banach space",
      "proper representation",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6373G"
    }
  }
}