{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23",
  "labels": {
    "zh-CN": "向量场",
    "en": "vector field"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "bbbbfeb8b5e7856bc57fd4a4372d8d762ee4b72db63ef06c3e0f7e8839b9f325",
  "occurrences": [
    {
      "concept_id": "urn:uuid:85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-15/03-tangent-cotangent-and-tensor-spaces",
      "anchor": "concept-15-vector-field",
      "chapter": "15",
      "section": "15.3",
      "offset": 15134,
      "range": [
        21977,
        22207
      ],
      "source_revision": "42521000e4d5202ad14e779d03d39e10558dce1e3f583880e73256da77dce50d",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "向量场(vector field)",
      "context": {
        "range": [
          21974,
          22470
        ],
        "quote": "一个 <u id=\"concept-15-vector-field\" class=\"concept-term\" data-concept-identity=\"urn:uuid:85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23\" data-concept-route=\"/concept-identities#concept-85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23\">向量场(vector field)</u> $X$ 是在每一点 $p \\in M$ 处指定一个切向量 $X _ { p }$ 的对应关系。换言之，$X$ 是从 $M$ 到集合 $\\textstyle \\bigcup _ { p \\in M } T _ { p } ( M )$ 的映射，其性质是每一点的像 $X ( p )$ 都属于 $p$ 处的切空间 $T _ { p } ( M )$。因此我们可以用 $X _ { p }$ 代替 $X ( p )$。若对每个可微函数 $f \\in { \\mathcal { F } } ( M )$，由下式定义的函数 $X f$",
        "quote_sha256": "15dd29619f00b7c3819d987f92c3f5c985a753bbf549046121403ff3eac69e64",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-15/03-tangent-cotangent-and-tensor-spaces",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-c9ed780ef3ac8822bbd34886"
    },
    {
      "concept_id": "urn:uuid:85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-15/03-tangent-cotangent-and-tensor-spaces",
      "anchor": "first-9c7d421876a7463f4c22-en",
      "chapter": "15",
      "section": "15.3",
      "offset": 19215,
      "range": [
        25543,
        25774
      ],
      "source_revision": "8b0278d73f794378de0c8f3aa32c9c14db7ce60b01ab8b11faed63d6d00fda5f",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "vector field",
      "context": {
        "range": [
          25541,
          26280
        ],
        "quote": "A <u class=\"concept-term\" data-concept-identity=\"urn:uuid:85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23\" data-concept-route=\"/concept-identities#concept-85e79af6-5c6d-4e9b-b6b4-4ed3060bfd23\" id=\"first-9c7d421876a7463f4c22-en\">vector field</u> $X$ is an assignment of a tangent vector $X _ { p }$ at each point $p \\in M$ . In other words, $X$ is a map from $M$ to the set $\\textstyle \\bigcup _ { p \\in M } T _ { p } ( M )$ with the property that the image of every point, $X ( p )$ , belongs to the tangent space $T _ { p } ( M )$ at $p$ . We may thus write $X _ { p }$ in place of $X ( p )$ . The vector field is said to be differentiable or smooth if for every differentiable function $f \\in { \\mathcal { F } } ( M )$ the function $X f$ defined by",
        "quote_sha256": "5ce9794d8ace32f164b82d71be6a2ce3b7d3ca6b2b7079820dc9192111800c5e",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-15/03-tangent-cotangent-and-tensor-spaces",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-d0176743115d88192c39a7dd"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-15/03-tangent-cotangent-and-tensor-spaces",
      "lang": "en",
      "section": "15.3",
      "signal": "term-mark",
      "label": "vector field",
      "english": "vector field",
      "offset": 18571
    },
    {
      "route": "zh/chapter-15/03-tangent-cotangent-and-tensor-spaces",
      "lang": "zh-CN",
      "section": "15.3",
      "signal": "term-mark",
      "label": "向量场",
      "english": "vector field",
      "offset": 14595
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-c9ed780ef3ac8822bbd34886",
    "occ-d0176743115d88192c39a7dd"
  ],
  "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": "05d37b7b778c56aad21e8e18a03147be9390aa8389d595ee64f2271935d658c0",
  "optional_enrichments": []
}