{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "2CG46QFBHW"
    }
  ],
  "body": "\n## Summary\n\nThe Vietoris topology is a topology on a set of subsets of a topological space, usually the closed subsets or the compact subsets.\nA set is near a set $A$ when it lies inside a given open neighbourhood of $A$.\nIt must also meet some given open sets that $A$ meets.\nIt turns a family of subsets into a space, called a hyperspace.\nOn the nonempty compact subsets of a metric space, it is the topology of the Hausdorff metric.\n\n## Explanations\n\n### L1 human\n\nSometimes the objects you want to move around are sets, not points.\nThe Vietoris topology says when two sets are close.\nA set $B$ is close to $A$ when $B$ stays inside a thin open region around $A$, and $B$ reaches every part of $A$ you chose to watch.\nFor example, in the plane, a fine grid of points inside a disc is close to the disc in this sense.\n",
  "commit": "efe85cee8dbc57d85bedbacfb97b99d1b7bee843",
  "front": {
    "kind": "concept",
    "msc": [
      "54B20"
    ],
    "name": "Vietoris topology",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Hypertopology"
      }
    ],
    "specializes": [
      "0CQHFPGJ45"
    ],
    "tag": "BJVRFFJTV6"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/BJVRFFJTV6/",
  "links": [
    {
      "field": "specializes",
      "target": "0CQHFPGJ45"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/BJVRFFJTV6.md",
  "msc": [
    "54B20"
  ],
  "name": "Vietoris topology",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/BJV/BJVRFFJTV6.md",
  "status": null,
  "tag": "BJVRFFJTV6",
  "uri": "m2://BJVRFFJTV6",
  "url": "https://math2.tamnd.com/wiki/vietoris-topology/",
  "writing": {
    "tag": "BJVRFFJTV6",
    "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
      }
    ]
  }
}