{
  "id": "math/0509607",
  "version": "v1",
  "published": "2005-09-26T04:42:07.000Z",
  "updated": "2005-09-26T04:42:07.000Z",
  "title": "o-Boundedness of free objects over a Tychonoff space",
  "authors": [
    "Lyubomyr Zdomskyy"
  ],
  "comment": "20 pages; Latex2e; Submitted to Matematychni Studii",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we characterize [strict] o-boundedness of the free (abelian) topological group F(X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l-invariant. This gives a method of construction of OF-undetermined topological groups with strong combinatorial properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-26T04:42:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tychonoff space",
      "free objects",
      "o-boundedness",
      "free locally-convex linear topological space",
      "topological group"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9607Z"
    }
  }
}