{
  "id": "1009.1676",
  "version": "v2",
  "published": "2010-09-09T02:48:16.000Z",
  "updated": "2012-05-16T02:12:59.000Z",
  "title": "On the topology of free paratopological groups",
  "authors": [
    "Ali Sayed Elfard",
    "Peter Nickolas"
  ],
  "comment": "http://blms.oxfordjournals.org/cgi/content/abstract/bds031?ijkey=9Su2bYV9e19JMxf&keytype=ref",
  "doi": "10.1112/blms/bds031",
  "categories": [
    "math.GN"
  ],
  "abstract": "The result often known as Joiner's lemma is fundamental in understanding the topology of the free topological group $F(X)$ on a Tychonoff space$X$. In this paper, an analogue of Joiner's lemma for the free paratopological group $\\FP(X)$ on a $T_1$ space $X$ is proved. Using this, it is shown that the following conditions are equivalent for a space $X$: (1) $X$ is $T_1$; (2) $\\FP(X)$ is $T_1$; (3) the subspace $X$ of $\\FP(X)$ is closed; (4) the subspace $X^{-1}$ of $\\FP(X)$ is discrete; (5) the subspace $X^{-1}$ is $T_1$; (6) the subspace $X^{-1}$ is closed; and (7) the subspace $\\FP_n(X)$ is closed for all $n \\in \\N$, where $\\FP_n(X)$ denotes the subspace of $\\FP(X)$ consisting of all words of length at most $n$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-16T02:12:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A30",
      "54D10",
      "54E99",
      "54H99"
    ],
    "keywords": [
      "free paratopological group",
      "joiners lemma",
      "tychonoff space",
      "free topological group",
      "equivalent"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1676S"
    }
  }
}