{
  "id": "math/0511645",
  "version": "v1",
  "published": "2005-11-26T19:54:12.000Z",
  "updated": "2005-11-26T19:54:12.000Z",
  "title": "The space of intervals in a Euclidean space",
  "authors": [
    "Shingo Okuyama"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-62.abs.html",
  "journal": "Algebr. Geom. Topol. 5 (2005) 1555-1572",
  "categories": [
    "math.AT"
  ],
  "abstract": "For a path-connected space X, a well-known theorem of Segal, May and Milgram asserts that the configuration space of finite points in R^n with labels in X is weakly homotopy equivalent to the n-th loop-suspension of X. In this paper, we introduce a space I_n(X) of intervals suitably topologized in R^n with labels in a space X and show that it is weakly homotopy equivalent to n-th loop-suspension of X without the assumption on path-connectivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-26T19:54:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "55P40"
    ],
    "keywords": [
      "euclidean space",
      "weakly homotopy equivalent",
      "n-th loop-suspension",
      "well-known theorem",
      "milgram asserts"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}