{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:06fabb9a-f268-4d2b-8732-263ac9213a4d",
  "labels": {
    "zh-CN": "康托尔集",
    "en": "Cantor set"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "e1a3ea0d2300281ecf2d174513d064ffd37e37a22230fcaa8d2139df1760c5a1",
  "occurrences": [
    {
      "concept_id": "urn:uuid:06fabb9a-f268-4d2b-8732-263ac9213a4d",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-01/05-infinite-sets",
      "anchor": "first-827e033327040d2a58e4-zh",
      "chapter": "1",
      "section": "1.5",
      "offset": 5597,
      "range": [
        10226,
        10461
      ],
      "source_revision": "de98ef3b57633eb615044c4c10101bc445e6695597e0d0703fc5fd583f6a2664",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "康托尔集(Cantor set)",
      "context": {
        "range": [
          10097,
          11181
        ],
        "quote": "> [!example] <a class=\"object-permalink\" href=\"#example-1-11\">例 1.11</a> · 康托尔集\n>\n> 在 $[0,1]$ 中取那些**存在只使用数字 $0$、$2$ 的三进制展开**的数，得到<u class=\"concept-term\" data-concept-identity=\"urn:uuid:06fabb9a-f268-4d2b-8732-263ac9213a4d\" data-concept-route=\"/concept-identities#concept-06fabb9a-f268-4d2b-8732-263ac9213a4d\" id=\"first-827e033327040d2a58e4-zh\">康托尔集(Cantor set)</u> $C$。也可以从 $[0,1]$ 中删去中间开三分之一 $(1/3,2/3)$，再删去剩余每段的中间开三分之一，如此无限继续。\n>\n> <span id=\"figure-1-2\" class=\"block-anchor\"></span>\n>\n> ![图 1.2：康托尔集的前四次构造](../../assets/chapter-01/dd380d002c6d44db5e0cb3b728608ee0328279de53edc99daa418ed0042af4aa.jpg)\n> *图 1.2 · 前四次删除后的区间。*\n>\n> 每个 $0$–$1$ 序列 $(\\epsilon_i)$ 唯一地给出 $C$ 中的点 $\\sum_{i\\geq1}2\\epsilon_i3^{-i}$，所以 $C$ 与 $2^{\\mathbb N}$ 一一对应，是不可数的；但它又是<u class=\"concept-term\" data-concept-identity=\"urn:uuid:be9d7d7b-195a-4a88-864a-6fd1e6eaf2f7\" data-concept-route=\"/concept-identities#concept-be9d7d7b-195a-4a88-864a-6fd1e6eaf2f7\" id=\"first-1573c974299f73854745-zh\">无处稠密(nowhere dense)</u>的。将所有三进制数字 $2$ 换成二进制数字 $1$ 得到的实数对应并非单射，须区分“二进制序列”和“具有重复展开的实数”。\n>\n> 这种结构不只是数学奇观，与物理有关的非线性映射也会自然产生类似集合。",
        "quote_sha256": "d6d09318ad75fa886e05631539516ac4dcecc9a803626d1167fb0a89b7971bb8",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-01/05-infinite-sets",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-08cf19db9d060c5093fc6e60"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-01/05-infinite-sets",
      "lang": "zh-CN",
      "section": "1.5",
      "signal": "term-mark",
      "label": "康托尔集",
      "english": "Cantor set",
      "offset": 4669
    }
  ],
  "statements": [],
  "resolved_references": [
    {
      "raw": "href=\"#example-1-11\"",
      "href": "#example-1-11",
      "range": [
        10138,
        10158
      ],
      "relation": "references",
      "target_route": "zh/chapter-01/05-infinite-sets",
      "target_anchor": "example-1-11",
      "resolved": true,
      "reason": null,
      "source_revision": "de98ef3b57633eb615044c4c10101bc445e6695597e0d0703fc5fd583f6a2664",
      "source_route": "zh/chapter-01/05-infinite-sets",
      "occurrence_id": "occ-08cf19db9d060c5093fc6e60"
    }
  ],
  "reading_order": [
    "occ-08cf19db9d060c5093fc6e60"
  ],
  "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": "959623cbbc94ca150c2b8e185b6b49e6d032b72ff97747ef70bb5adc8ae3fd8f",
  "optional_enrichments": []
}