{
  "aliases": [
    "simply-connected-space"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "075C629XTH"
    }
  ],
  "body": "\n## Summary\n\nA simply connected domain is a path-connected set in which each closed loop can be shrunk continuously to a point without leaving the set.\nInformally, the set is in one piece and has no hole that a loop can go around.\nOn such domains, curl-free vector fields are conservative.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "aliases": [
      "simply-connected-space"
    ],
    "kind": "concept",
    "msc": [
      "55Q05"
    ],
    "name": "Simply connected domain",
    "same_as": {
      "wikidata": "Q912058",
      "wikipedia": "Simply connected space"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Simply_connected_space"
      }
    ],
    "tag": "0QW64ARSHB"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0QW64ARSHB/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0QW64ARSHB.md",
  "msc": [
    "55Q05"
  ],
  "name": "Simply connected domain",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0QW/0QW64ARSHB.md",
  "status": null,
  "tag": "0QW64ARSHB",
  "uri": "m2://0QW64ARSHB",
  "url": "https://math2.tamnd.com/wiki/simply-connected-domain/",
  "writing": {
    "tag": "0QW64ARSHB",
    "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
      }
    ]
  }
}