{
  "id": "2208.10619",
  "version": "v1",
  "published": "2022-08-22T21:56:19.000Z",
  "updated": "2022-08-22T21:56:19.000Z",
  "title": "Stability of the q-hyperconvex hull of a quasi-metric space",
  "authors": [
    "Nicolò Zava"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "In this paper, we study the stability of the q-hyperconvex hull of a quasi-metric space, adapting known results for the hyperconvex hull of a metric space. To pursue this goal, we extend well-known metric notions, such as Gromov-Hausdorff distance and rough isometries, to the realm of quasi-metric spaces. In particular, we prove that two q-hyperconvex hulls are close with respect to the Gromov-Hausdorff distance if so are the original spaces. Moreover, we provide an intrinsic characterisation of those spaces that are Sym-large in their q-hyperconvex hulls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-22T21:56:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E35",
      "51F30",
      "53C23",
      "54D35"
    ],
    "keywords": [
      "q-hyperconvex hull",
      "quasi-metric space",
      "extend well-known metric notions",
      "gromov-hausdorff distance",
      "rough isometries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}