{
  "id": "1105.4009",
  "version": "v2",
  "published": "2011-05-20T03:56:15.000Z",
  "updated": "2014-04-03T11:10:57.000Z",
  "title": "On topological fundamental groups of quotient spaces",
  "authors": [
    "Hamid Torabi",
    "Ali Pakdaman",
    "Behrooz Mashayekhy"
  ],
  "comment": "13 pages, 1 figure, to appear in Ukrainian Mathematical Journal",
  "categories": [
    "math.AT",
    "math.GN"
  ],
  "abstract": "Let $p:X\\rightarrow X/A$ be a quotient map, where $A$ is a subspace of $X$. We explore conditions under which $p_*(\\pi_1^{qtop}(X,x_0))$ is dense in $\\pi_1^{qtop}(X/A,*))$, where the fundamental groups enjoy the natural quotient topology inherited from the loop space and $p_*$ is the induced continuous homomorphism by the quotient map $p$. Also, we give some applications to find out some properties for $\\pi_1^{qtop}(X/A,*)$. In particular, we give some conditions in which $\\pi_1^{qtop}(X/A,*)$ is an indiscrete topological group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-03T11:10:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P65",
      "55Q52",
      "55Q70"
    ],
    "keywords": [
      "topological fundamental groups",
      "quotient spaces",
      "quotient map",
      "fundamental groups enjoy",
      "natural quotient topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.4009T"
    }
  }
}