{
  "id": "math/0609665",
  "version": "v1",
  "published": "2006-09-23T19:47:59.000Z",
  "updated": "2006-09-23T19:47:59.000Z",
  "title": "A separable manifold failing to have the homotopy type of a CW-complex",
  "authors": [
    "Alexandre Gabard"
  ],
  "comment": "5 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the Pr\\\"ufer surface, which is a separable non-metrizable 2-manifold, has not the homotopy type of a CW-complex. This will follow easily from J. H. C. Whitehead's result: if one has a good approximation of an arbitrary space by a CW-complex, which fails to be a homotopy equivalence, then the given space is not homotopy equivalent to a CW-complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-23T19:47:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N05",
      "57Q05"
    ],
    "keywords": [
      "homotopy type",
      "separable manifold failing",
      "cw-complex",
      "whiteheads result",
      "arbitrary space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9665G"
    }
  }
}