{
  "id": "1110.0082",
  "version": "v2",
  "published": "2011-10-01T07:25:19.000Z",
  "updated": "2012-03-04T05:36:52.000Z",
  "title": "On rectifiable spaces and paratopological groups",
  "authors": [
    "Fucai Lin",
    "Rongxin Shen"
  ],
  "comment": "19 pages (replace)",
  "journal": "Topology and its Applications, 158(2011), 597-610",
  "doi": "10.1016/j.topol.2010.12.008",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "We mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If $A$ and $B$ are $\\omega$-narrow subsets of a paratopological group $G$, then $AB$ is $\\omega$-narrow in $G$, which give an affirmative answer for \\cite[Open problem 5.1.9]{A2008}; (2) Every bisequential or weakly first-countable rectifiable space is metrizable; (3) The properties of Fr$\\acute{e}$chet-Urysohn and strongly Fr$\\acute{e}$chet-Urysohn are coincide in rectifiable spaces; (4) Every rectifiable space $G$ contains a (closed) copy of $S_{\\omega}$ if and only if $G$ has a (closed) copy of $S_{2}$; (5) If a rectifiable space $G$ has a $\\sigma$-point-discrete closed $k$-network, then $G$ contains no closed copy of $S_{\\omega_{1}}$; (6) If a rectifiable space $G$ is pointwise canonically weakly pseudocompact, then $G$ is a Moscow space. Also, we consider the remainders of paratopological groups or rectifiable spaces, and give a partial answer to questions posed by C. Liu in \\cite{Liu2009} and C. Liu, S. Lin in \\cite{Liu20091}, respectively.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-04T05:36:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A25",
      "54B05",
      "54E20",
      "54E35"
    ],
    "keywords": [
      "paratopological group",
      "narrow subsets",
      "cardinal invariants",
      "chet-urysohn",
      "generalized metric properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.0082L"
    }
  }
}