{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:b997f55f-72cd-41dd-a707-f2a61744a707",
  "labels": {
    "zh-CN": "边缘群",
    "en": "boundary group"
  },
  "alternative_labels": [
    {
      "lang": "en",
      "value": "p-boundary group"
    },
    {
      "lang": "en",
      "value": "r-boundary group"
    },
    {
      "lang": "zh-CN",
      "value": "$p$-边界群"
    },
    {
      "lang": "zh-CN",
      "value": "$p$-边缘群"
    },
    {
      "lang": "zh-CN",
      "value": "$r$-边界群"
    },
    {
      "lang": "zh-CN",
      "value": "$r$-边缘群"
    },
    {
      "lang": "zh-CN",
      "value": "边界群"
    }
  ],
  "scope_note": "§17.4: the subgroup B_p = im ∂_{p+1} of p-boundaries in a chain complex.",
  "identity_status": "active",
  "identity_revision": "c669e04b9e255e3c641e72e7fd37a53e4611b9c0bef624861e10885cc3d0a43c",
  "occurrences": [
    {
      "concept_id": "urn:uuid:b997f55f-72cd-41dd-a707-f2a61744a707",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-17/04-homology-and-cohomology",
      "anchor": "first-14f4d6dbed8b0089f13d-zh",
      "chapter": "17",
      "section": "17.4",
      "offset": 9950,
      "range": [
        14247,
        14283
      ],
      "source_revision": "062d2117b72e7e8394304765fe808ba3c64d7a0bedab04398314d109ba588d33",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "registered-first-position"
      },
      "label": "",
      "context": {
        "range": [
          14247,
          14433
        ],
        "quote": "<span id=\"first-14f4d6dbed8b0089f13d-zh\" class=\"block-anchor\"></span>若令 $B _ { p } ( M )$ 为 $M ,$ 上所有 $p$-边界的集合，而 $Z _ { p } ( M )$ 为所有 $p$-循环，则二者都是 $\\mathcal { C } _ { p } ( M )$ 的向量子空间",
        "quote_sha256": "4d37628f66207c2802c03fc8b8f4127eca97a97779ebce4fe454e75e271a5a0f",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-17/04-homology-and-cohomology",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-39b78ec184a609a293dd5cf5"
    },
    {
      "concept_id": "urn:uuid:b997f55f-72cd-41dd-a707-f2a61744a707",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-17/04-homology-and-cohomology",
      "anchor": "first-14f4d6dbed8b0089f13d-en",
      "chapter": "17",
      "section": "17.4",
      "offset": 12403,
      "range": [
        16227,
        16263
      ],
      "source_revision": "5767cb43706053d76f0ed42e33b7b4da3a4b2183914f883d768ba063b526ebb8",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "registered-first-position"
      },
      "label": "",
      "context": {
        "range": [
          16227,
          16471
        ],
        "quote": "<span id=\"first-14f4d6dbed8b0089f13d-en\" class=\"block-anchor\"></span>If we let $B _ { p } ( M )$ be the set of all $p$-boundaries on $M ,$ , and $Z _ { p } ( M )$ all $p$-cycles, these are both vector subspaces of $\\mathcal { C } _ { p } ( M )$",
        "quote_sha256": "b2b5031971cd44b09f834eb59c2803ca016373458b787ef903841e6cf26405e8",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-17/04-homology-and-cohomology",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-ae48f3f1490ce06e490de532"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-17/04-homology-and-cohomology",
      "lang": "en",
      "section": "17.4",
      "signal": "term-mark",
      "label": "boundary group",
      "english": "boundary group",
      "offset": 10797
    },
    {
      "route": "zh/chapter-17/04-homology-and-cohomology",
      "lang": "zh-CN",
      "section": "17.4",
      "signal": "term-mark",
      "label": "边缘群",
      "english": "boundary group",
      "offset": 8483
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-39b78ec184a609a293dd5cf5",
    "occ-ae48f3f1490ce06e490de532"
  ],
  "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": "5550d03c0b6c43fbc61b89a25bdca56d907e0f783233412884198c610828e4f1",
  "optional_enrichments": []
}
