{
  "id": "1808.00272",
  "version": "v1",
  "published": "2018-08-01T11:20:09.000Z",
  "updated": "2018-08-01T11:20:09.000Z",
  "title": "Automatic continuity of $\\aleph_1$-free groups",
  "authors": [
    "Samuel M. Corson"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that groups for which every countable subgroup is free ($\\aleph_1$-free groups) are n-slender, cm-slender, and lcH-slender. In particular every homomorphism from a completely metrizable group to an $\\aleph_1$-free group has an open kernel. We also show that $\\aleph_1$-free abelian groups are lcH-slender, which is especially interesting in light of the fact that some $\\aleph_1$-free abelian groups are neither n- nor cm-slender. The strongly $\\aleph_1$-free abelian groups are shown to be n-, cm-, and lcH-slender. We also give a characterization of cm- and lcH-slender abelian groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-01T11:20:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K20",
      "03E75",
      "22A05",
      "22B05"
    ],
    "keywords": [
      "free group",
      "free abelian groups",
      "automatic continuity",
      "lch-slender abelian groups",
      "open kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}