{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0NVPNC12JY"
    },
    {
      "field": "uses",
      "target": "34SN01NWPS"
    },
    {
      "field": "uses",
      "target": "7QFKD5JXH6"
    },
    {
      "field": "uses",
      "target": "99GNAS98PV"
    },
    {
      "field": "uses",
      "target": "DV8GH6HJJ8"
    },
    {
      "field": "uses",
      "target": "ETDW4AK1W1"
    },
    {
      "field": "uses",
      "target": "HTDYK465JA"
    },
    {
      "field": "uses",
      "target": "J8QBXGP7KK"
    },
    {
      "field": "uses",
      "target": "JX3ZH5WY0T"
    },
    {
      "field": "uses",
      "target": "KK8KZQNDVY"
    },
    {
      "field": "uses",
      "target": "M44J4ZJ6Z8"
    },
    {
      "field": "uses",
      "target": "NKKYW7Z6R7"
    },
    {
      "field": "uses",
      "target": "P2F66BS71T"
    },
    {
      "field": "uses",
      "target": "T4MTXNJJ3Q"
    },
    {
      "field": "uses",
      "target": "TX1W8PRASW"
    },
    {
      "field": "uses",
      "target": "ZH29VRRRJ6"
    }
  ],
  "body": "\n## Summary\n\nAn open cover of a subset of a topological space is a family of open sets whose union contains the subset.\nOpen covers are used to define compactness.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "1906G9J52Q"
    ],
    "kind": "concept",
    "msc": [
      "54D30"
    ],
    "name": "Open cover",
    "sources": [
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Cover_(topology)"
      }
    ],
    "tag": "049PXYHW1T"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/049PXYHW1T/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/049PXYHW1T.md",
  "msc": [
    "54D30"
  ],
  "name": "Open cover",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/049/049PXYHW1T.md",
  "status": null,
  "tag": "049PXYHW1T",
  "uri": "m2://049PXYHW1T",
  "url": "https://tamnd.github.io/math2/wiki/open-cover/",
  "writing": {
    "tag": "049PXYHW1T",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
