{
  "id": "2210.17280",
  "version": "v1",
  "published": "2022-10-31T13:02:59.000Z",
  "updated": "2022-10-31T13:02:59.000Z",
  "title": "The homeomorphism group of a surface without boundary is minimal",
  "authors": [
    "J. de la Nuez González"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the compact-open topology is the unique Hausdorff separable group topology on the group if the surface is closed or the complement in a closed surface of either a finite set or the union of a finite set and a Cantor set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-31T13:02:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S05",
      "57N99"
    ],
    "keywords": [
      "homeomorphism group",
      "compact-open topology",
      "finite set",
      "unique hausdorff separable group topology",
      "hausdorff group topology strictly coarser"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}