{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "EK0FJBNE1Q"
    },
    {
      "field": "instance_of",
      "target": "VGCTDCGS6V"
    }
  ],
  "body": "\n## Summary\n\nAn indecomposable continuum is a [[continuum|NJQ196M1WR]] that is not the union of two proper subcontinua.\nFamiliar continua such as arcs, circles and discs are decomposable, so the indecomposable ones are a source of strange examples.\nThey appear in plane topology, as common boundaries of domains, and in dynamics, as attractors.\n\n## Explanations\n\n### L1 human\n\nThe interval $[0, 1]$ is the union of the two smaller pieces $[0, 1/2]$ and $[1/2, 1]$, each a continuum.\nAn indecomposable continuum cannot be cut up like this: any two smaller continua inside it leave something out.\nPictures of them look like infinitely many strands wound back and forth, such as the Knaster bucket handle.\nThe [[pseudo-arc|VGCTDCGS6V]] is an extreme case, where every subcontinuum is again indecomposable.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "54F15"
    ],
    "name": "Indecomposable continuum",
    "same_as": {
      "wikidata": "Q2995675",
      "wikipedia": "Indecomposable continuum"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Indecomposable_continuum"
      }
    ],
    "specializes": [
      "NJQ196M1WR"
    ],
    "tag": "56J7DSVAZH"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/56J7DSVAZH/",
  "links": [
    {
      "field": "specializes",
      "target": "NJQ196M1WR"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/56J7DSVAZH.md",
  "msc": [
    "54F15"
  ],
  "name": "Indecomposable continuum",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/56J/56J7DSVAZH.md",
  "status": null,
  "tag": "56J7DSVAZH",
  "uri": "m2://56J7DSVAZH",
  "url": "https://math2.tamnd.com/wiki/indecomposable-continuum/",
  "writing": {
    "tag": "56J7DSVAZH",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}
