{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "DHYSPSYSCB"
    },
    {
      "field": "uses",
      "target": "YGSKZFTEX1"
    },
    {
      "field": "defines",
      "target": "TS5XH58X86"
    },
    {
      "field": "about",
      "target": "YGSKZFTEX1"
    }
  ],
  "body": "\n## Summary\n\nGromov–Hausdorff convergence is a notion of convergence for sequences of metric spaces, not of points inside one space.\nA sequence of compact metric spaces converges when its distance to the limit in the [[Gromov–Hausdorff space|ETRF2FHAEE]] tends to zero.\nIt lets one take limits of Riemannian manifolds, and such limits are often singular spaces.\nIt is a basic tool of metric and synthetic methods in global geometry.\n\n## Explanations\n\n### L1 human\n\nThink of shapes seen from far away, where only distances matter.\nTwo shapes are close when they can be laid in a common space so that each lies near the other.\nA sequence of shapes converges when this closeness tends to zero.\nFor example, the points $0, \\tfrac{1}{n}, \\tfrac{2}{n}, \\ldots, 1$ form finite spaces that converge to the segment $[0, 1]$.\nA thin tube around a circle also converges to the circle when the tube gets thinner.\n",
  "commit": "efe85cee8dbc57d85bedbacfb97b99d1b7bee843",
  "front": {
    "kind": "concept",
    "msc": [
      "53C23",
      "54E35"
    ],
    "name": "Gromov–Hausdorff convergence",
    "same_as": {
      "wikidata": "Q929777",
      "wikipedia": "Gromov–Hausdorff convergence"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Gromov%E2%80%93Hausdorff_convergence"
      }
    ],
    "tag": "GT56RTG9X5"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/GT56RTG9X5/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/GT56RTG9X5.md",
  "msc": [
    "53C23",
    "54E35"
  ],
  "name": "Gromov–Hausdorff convergence",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/GT5/GT56RTG9X5.md",
  "status": null,
  "tag": "GT56RTG9X5",
  "uri": "m2://GT56RTG9X5",
  "url": "https://math2.tamnd.com/wiki/gromov-hausdorff-convergence/",
  "writing": {
    "tag": "GT56RTG9X5",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}