{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:b2da5ce9-fdbc-4d32-9495-60eba58b0cab",
  "labels": {
    "zh-CN": "函数空间",
    "en": "function space"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "82da4fb124ceb6906be55a6b57a46985bf964246167de8c48ae4f94ddb7031f6",
  "occurrences": [
    {
      "concept_id": "urn:uuid:b2da5ce9-fdbc-4d32-9495-60eba58b0cab",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/03-unitary-group-representations",
      "anchor": "first-467fca2b7844dc4bfc62-zh",
      "chapter": "1",
      "section": "1.3",
      "offset": 8851,
      "range": [
        20395,
        20708
      ],
      "source_revision": "4ee587fc4d72d2916ca8f6bce8080ecd42e2ae3d45d92d067027a95982f00008",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "函数空间(function space)",
      "context": {
        "range": [
          20283,
          21276
        ],
        "quote": "现代数学的一条基本思想是：若把空间 $M$ 看作由若干点组成，那么理解 $M$ 的一种方式是研究<span id=\"concept-1-function-space\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-function-space\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:b2da5ce9-fdbc-4d32-9495-60eba58b0cab\" data-concept-route=\"/concept-identities#concept-b2da5ce9-fdbc-4d32-9495-60eba58b0cab\" id=\"first-467fca2b7844dc4bfc62-zh\">函数空间(function space)</u> $F(M)$，也就是定义在 $M$ 上的函数所构成的集合。这样便将问题“<span id=\"concept-1-linearize\" class=\"block-anchor\"></span><span id=\"concept-1-linearization\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-id=\"concept-1-linearization\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:39c83087-8f6e-4028-bca4-e15886984c77\" data-concept-route=\"/concept-identities#concept-39c83087-8f6e-4028-bca4-e15886984c77\" id=\"first-add16b5bc60391c7391b-zh\">线性化(linearize)</u>”了，因为无论原点集具有怎样的几何结构，函数空间都是向量空间。若点集有限，函数空间就是有限维向量空间；一般而言，它是无限维的，还需要进一步说明所考虑的函数空间类型（例如连续函数、可微函数或范数有限的函数）。",
        "quote_sha256": "d24c98b9a47f465f294d5e8dec5163580cad8667676a14fd196462ed9e5806eb",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-01/03-unitary-group-representations",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-d2a95c7565da33304b1f897f"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/03-unitary-group-representations",
      "lang": "zh-CN",
      "section": "1.3",
      "signal": "term-mark",
      "label": "函数空间",
      "english": "function space",
      "offset": 5425
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-d2a95c7565da33304b1f897f"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "095f993d132543fd1086c4b0ddb76915cbd3a298e3f7b027c70e602f3415136e",
  "optional_enrichments": []
}