{
  "id": "enwiki-001300229338",
  "slug": "smooth-structure",
  "title": "Smooth structure",
  "qid": "",
  "lead": "In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows mathematical analysis to be performed on the manifold.",
  "body": "In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows mathematical analysis to be performed on the manifold. If \\mu and \\nu are two maximal atlases on M the two smooth structures associated to \\mu and \\nu are said to be equivalent if there is a diffeomorphism f : M \\to M such that \\mu \\circ f = \\nu. == See also==",
  "categories": [
    "20353112",
    "22906070",
    "23118434",
    "23603337",
    "24745122",
    "27653916",
    "81199107"
  ],
  "license": "CC BY-SA 4.0",
  "source_uri": "https://en.wikipedia.org/w/index.php?oldid=1300229338",
  "content_hash": "",
  "created_at": null,
  "updated_at": 1752365482.0,
  "claims": [],
  "contradictions": [],
  "confidence": 0.6,
  "csl": {
    "id": "enwiki-001300229338",
    "type": "webpage",
    "title": "Smooth structure",
    "author": [
      {
        "family": "Anticloud FZ LLE",
        "literal": "Anticloud FZ LLE"
      }
    ],
    "container-title": "encyclopegia.org",
    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
    "URL": "https://encyclopegia.org/a/smooth-structure",
    "issued": {
      "date-parts": [
        [
          2026,
          11,
          15
        ]
      ]
    },
    "accessed": {
      "date-parts": [
        [
          2026,
          11,
          15
        ]
      ]
    },
    "license": "CC BY-SA 4.0",
    "DOI": "eo1:enwiki-001300229338",
    "isBasedOn": "https://en.wikipedia.org/w/index.php?oldid=1300229338",
    "note": "Immutable snapshot enwiki-001300229338"
  }
}