{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:7c7c4b86-63b1-451e-b0be-15f02ebca981", "labels": { "zh-CN": "贝蒂数", "en": "Betti number" }, "alternative_labels": [ { "lang": "zh-CN", "value": "Betti数" } ], "scope_note": "", "identity_status": "active", "identity_revision": "4304888b9b8c217eb80971bf7b43ece6e80a2a5181165a5c62b53b6fb00b6a9c", "occurrences": [ { "concept_id": "urn:uuid:7c7c4b86-63b1-451e-b0be-15f02ebca981", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-17/04-homology-and-cohomology", "anchor": "first-fc63cc448792993af149-zh", "chapter": "17", "section": "17.4", "offset": 11093, "range": [ 15390, 15626 ], "source_revision": "962da89618680522177106de9b1899c86eb3dedc9484f12c33659d432388a117", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "贝蒂数(Betti number)", "context": { "range": [ 14780, 15627 ], "quote": "通常这被称为第$p$个同调群(homology group)，其中只有阿贝尔群性质是相关的。若两个循环$C _ { 1 }$与$C _ { 2 }$属于同一个同调类，即存在一个链$C$使得$C _ { 1 } - C _ { 2 } = \\partial C$，则称它们是同调的(homologous)的。第$p$个同调空间的维数称为第$p$个贝蒂数(Betti number)，", "quote_sha256": "8de502e60460eae59becddbfdfb4feafece5152c148f3f7d22c008e6fa4e610f", "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-c09b5c5912809bbd36cb9e02" }, { "concept_id": "urn:uuid:7c7c4b86-63b1-451e-b0be-15f02ebca981", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-17/04-homology-and-cohomology", "anchor": "first-fc63cc448792993af149-en", "chapter": "17", "section": "17.4", "offset": 13780, "range": [ 17604, 17835 ], "source_revision": "bcdaffd9c93fa5d4dbb16ac427fef782512ff58c5d5472ea282c7769a2173a3d", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "Betti number", "context": { "range": [ 16808, 17836 ], "quote": "Commonly this is called the $p$th homology group, only the abelian group property being relevant. 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