{
  "id": "2003.06285",
  "version": "v1",
  "published": "2020-03-12T16:56:19.000Z",
  "updated": "2020-03-12T16:56:19.000Z",
  "title": "Branch points and stability",
  "authors": [
    "J. F. Jardine"
  ],
  "comment": "8 pages. arXiv admin note: substantial text overlap with arXiv:1908.06323",
  "categories": [
    "math.AT"
  ],
  "abstract": "The hierarchy poset and branch point poset for a data set both admit a calculus of least upper bounds. A method involving upper bounds is used to show that the map of branch points associated to the inclusion of data sets is a controlled homotopy equivalence, where the control is expressed by an upper bound relation that is constrained by Hausdorff distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-12T16:56:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U10",
      "68R10",
      "62H30"
    ],
    "keywords": [
      "data set",
      "branch point poset",
      "upper bound relation",
      "hausdorff distance",
      "controlled homotopy equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}