{
  "id": "1412.0447",
  "version": "v1",
  "published": "2014-12-01T12:14:23.000Z",
  "updated": "2014-12-01T12:14:23.000Z",
  "title": "Topologies induced by group actions",
  "authors": [
    "Jan Dobrowolski"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "We introduce some canonical topologies induced by actions of topological groups on groups and rings. For $H$ being a group [or a ring] and $G$ a topological group acting on $H$ as automorphisms, we describe the finest group [ring] topology on $H$ under which the action of $G$ on $H$ is continuous. We also study the introduced topologies in the context of Polish structures. In particular, we prove that there may be no Hausdorff topology on a group $H$ under which a given action of a Polish group on $H$ is continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-01T12:14:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topologies",
      "group actions",
      "topological group",
      "finest group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0447D"
    }
  }
}