{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:8e3f52f8-c41d-44c8-8648-f6ee019acffe",
  "labels": {
    "zh-CN": "微分同胚",
    "en": "diffeomorphism"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "bf7d6c2b0ee3b035c4571f05555febe06e7d8ca0d1a1c22df67c3d4a8b643757",
  "occurrences": [
    {
      "concept_id": "urn:uuid:8e3f52f8-c41d-44c8-8648-f6ee019acffe",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-15/02-differentiable-maps-and-curves",
      "anchor": "concept-15-diffeomorphism",
      "chapter": "15",
      "section": "15.2",
      "offset": 2154,
      "range": [
        5849,
        6084
      ],
      "source_revision": "5037af535ee57ea4c5199aeff4c34564cd8dcab00078f5418fed6e26fa937c27",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "微分同胚(diffeomorphism)",
      "context": {
        "range": [
          5847,
          6288
        ],
        "quote": "一个<u id=\"concept-15-diffeomorphism\" class=\"concept-term\" data-concept-identity=\"urn:uuid:8e3f52f8-c41d-44c8-8648-f6ee019acffe\" data-concept-route=\"/concept-identities#concept-8e3f52f8-c41d-44c8-8648-f6ee019acffe\">微分同胚(diffeomorphism)</u>是一个一一映射$\\alpha ; M \\to N$，且$\\alpha$与$\\alpha ^ { - 1 } : N \\to M$均可微。若存在微分同胚$\\alpha : M \\to N ;$，则称两个流形$M$与$N$微分同胚，记作$M \\cong N _ { \\mathrm { : } }$；当然，两个流形的维数必须相等，$m = n$。一个奇特而困难的事实是，存在具有多于一个不等价可微结构的拓扑流形。",
        "quote_sha256": "0fb21c8bed339878318daeaf4a6783f653e48e479900becfd07a95931c793bc3",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-15/02-differentiable-maps-and-curves",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-15f3a6a45676ac581ca28067"
    },
    {
      "concept_id": "urn:uuid:8e3f52f8-c41d-44c8-8648-f6ee019acffe",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-15/02-differentiable-maps-and-curves",
      "anchor": "first-c90ee60ec510dcc909d0-en",
      "chapter": "15",
      "section": "15.2",
      "offset": 3362,
      "range": [
        6547,
        6780
      ],
      "source_revision": "9fad1c5dead4be4f96f28153017d603fa581fca7205fefd292bbfdd4f9b262d4",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "diffeomorphism",
      "context": {
        "range": [
          6545,
          7253
        ],
        "quote": "A <u class=\"concept-term\" data-concept-identity=\"urn:uuid:8e3f52f8-c41d-44c8-8648-f6ee019acffe\" data-concept-route=\"/concept-identities#concept-8e3f52f8-c41d-44c8-8648-f6ee019acffe\" id=\"first-c90ee60ec510dcc909d0-en\">diffeomorphism</u> is a map $\\alpha ; M \\to N$ that is one-to-one and both $\\alpha$ and $\\alpha ^ { - 1 } : N \\to M$ are differentiable. Two manifolds $M$ and $N$ are said to be diffeomorphic, written $M \\cong N _ { \\mathrm { : } }$ if there exists a diffeomorphism $\\alpha : M \\to N ;$ ; the dimensions of the two manifolds must of course be equal, $m = n$ . It is a curious and difficult fact that there exist topological manifolds with more than one inequivalent differentiable structure.",
        "quote_sha256": "a1a35d6dcca040f9be976494ae82a1dac57e0b8f4d740dbe3f5c4af2a653d9d4",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-15/02-differentiable-maps-and-curves",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-e4caf06562cf1c49cf5b233d"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-15/02-differentiable-maps-and-curves",
      "lang": "en",
      "section": "15.2",
      "signal": "term-mark",
      "label": "diffeomorphism",
      "english": "diffeomorphism",
      "offset": 3362
    },
    {
      "route": "zh/chapter-15/02-differentiable-maps-and-curves",
      "lang": "zh-CN",
      "section": "15.2",
      "signal": "term-mark",
      "label": "微分同胚",
      "english": "diffeomorphism",
      "offset": 2154
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-15f3a6a45676ac581ca28067",
    "occ-e4caf06562cf1c49cf5b233d"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "9e7effd66f99ef1488e4bff71d524a4e16616cde09a4f324d791a24b148f05ed",
  "optional_enrichments": []
}
