{
  "id": "1011.5707",
  "version": "v1",
  "published": "2010-11-26T05:44:18.000Z",
  "updated": "2010-11-26T05:44:18.000Z",
  "title": "On Topological Homotopy Groups of $n$-Hawaiian like spaces",
  "authors": [
    "Fateme Helen Ghane",
    "Zainab Hamed",
    "Behrooz Mashayekhy",
    "Hanieh Mirebrahimi"
  ],
  "comment": "8 pages",
  "journal": "Topology Proceedings, Vol. 36, (2010) 255-266",
  "categories": [
    "math.AT"
  ],
  "abstract": "By an $n$-Hawaiian like space $X$ we mean the natural inverse limit, $\\displaystyle{\\varprojlim (Y_i^{(n)},y_i^*)}$, where $(Y_i^{(n)},y_i^*)=\\bigvee_{j\\leq i}(X_j^{(n)},x_j^*)$ is the wedge of $X_j^{(n)}$'s in which $X_j^{(n)}$'s are $(n-1)$-connected, locally $(n-1)$-connected, $n$-semilocally simply connected and compact CW spaces. In this paper, first we show that the natural homomorphism $\\displaystyle{\\beta_n:\\pi_n(X,*)\\rightarrow \\varprojlim \\pi_n(Y_i^{(n)},y_i^*)}$ is bijection. Second, using this fact we prove that the topological $n$-homotopy group of an $n$-Hawaiian like space, $\\pi_n^{top}(X,x^*)$, is a topological group for all $n\\geq 2$ which is a partial answer to the open question whether $\\pi_n^{top}(X,x^*)$ is a topological group for any space $X$ and $n\\geq 1$. Moreover, we show that $\\pi_n^{top}(X,x^*)$ is metrizable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-26T05:44:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q05",
      "55U40",
      "54H11",
      "55P35"
    ],
    "keywords": [
      "topological homotopy groups",
      "compact cw spaces",
      "natural inverse limit",
      "topological group",
      "open question"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5707G"
    }
  }
}