{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:5c98a7ca-5c42-4f2b-9236-86c453eddf68",
  "labels": {
    "zh-CN": "单射",
    "en": "injection"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "a9f0f31e4c4f0bcd68139003518b134cdf820c22cef47e4d7d380903d0fc10a3",
  "occurrences": [
    {
      "concept_id": "urn:uuid:5c98a7ca-5c42-4f2b-9236-86c453eddf68",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-01/04-mappings",
      "anchor": "first-5ec0092aba5eb3211c3a-zh",
      "chapter": "1",
      "section": "1.4",
      "offset": 3683,
      "range": [
        7372,
        7604
      ],
      "source_revision": "584fda344e534c6df3d98f8c4bf23c1a7c4695a49d55be41c192759946ba16fc",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "单射(injection)",
      "context": {
        "range": [
          7073,
          7974
        ],
        "quote": "\n> [!definition] 三类映射\n>\n> - **<u class=\"concept-term\" data-concept-identity=\"urn:uuid:2fe19f0b-4db1-4a5b-b7e1-dd0e6281d9a0\" data-concept-route=\"/concept-identities#concept-2fe19f0b-4db1-4a5b-b7e1-dd0e6281d9a0\" id=\"first-7e183040ab4a74c5973c-zh\">满射(surjection)</u>：**$\\varphi(X)=Y$，陪域中每个点都有原像。\n> - **<u class=\"concept-term\" data-concept-identity=\"urn:uuid:5c98a7ca-5c42-4f2b-9236-86c453eddf68\" data-concept-route=\"/concept-identities#concept-5c98a7ca-5c42-4f2b-9236-86c453eddf68\" id=\"first-5ec0092aba5eb3211c3a-zh\">单射(injection)</u>：**$\\varphi(x)=\\varphi(x')\\Rightarrow x=x'$，每个陪域点至多有一个原像。\n> - **<u class=\"concept-term\" data-concept-identity=\"urn:uuid:a0c09675-2669-4494-a712-c29017a7b391\" data-concept-route=\"/concept-identities#concept-a0c09675-2669-4494-a712-c29017a7b391\" id=\"first-9fdad7a27f354934cb46-zh\">双射(bijection)</u>：**既单射又满射，建立两个集合之间的一一对应。\n>\n> 只有双射才有定义在整个 $Y$ 上的逆映射 $\\varphi^{-1}:Y\\to X$。\n",
        "quote_sha256": "d9bae4be2db1028fc233837c6ceb17befa463a1047a9ea5311f0fa509c1a830b",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-01/04-mappings",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-98e04fe8898c6c7313758637"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-01/04-mappings",
      "lang": "zh-CN",
      "section": "1.4",
      "signal": "term-mark",
      "label": "单射",
      "english": "injection",
      "offset": 2078
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-98e04fe8898c6c7313758637"
  ],
  "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": "1494dbb7057b478f115ac7758be91249c600f9e68641e2e02f80a0f9426571e4",
  "optional_enrichments": []
}