{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:a0553dab-d811-417e-8a79-67ec620792e7", "labels": { "zh-CN": "可微流形", "en": "differentiable manifold" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "641b5515a6d8f8c35f35d5c0cb3205d8b3abbed279ae4ff1f4817da689772d3d", "occurrences": [ { "concept_id": "urn:uuid:a0553dab-d811-417e-8a79-67ec620792e7", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-15/01-differentiable-manifolds", "anchor": "concept-15-differentiable-manifold", "chapter": "15", "section": "15.1", "offset": 5485, "range": [ 10673, 10926 ], "source_revision": "4462fc8c20d8593a4fb08e421a831d99d655bb6a097fa3579d9c651b04f5672d", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "可微流形(differentiable manifold)", "context": { "range": [ 10027, 10938 ], "quote": "因此，任何图册 $\\boldsymbol { A }$ 都可以通过向其中添加所有与 的图卡 $C ^ { \\infty }$ 相容的图卡，从而扩展为一个 极大图册(maximal atlas)。这个极大图册称为 $M$ 上的一个 可微结构(differentiable structure)。若 $M$ 是一个 $n$ 维拓扑流形，且 是 $M ,$ 上的一个可微结构，则称有序对 $( M , A )$ 为一个 可微流形(differentiable manifold)；通常就简记为 $M$。", "quote_sha256": "35bbf2065b3aa4b2fd5196ec446208156775835abb4fcc654c49ff1a549874d5", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-15/01-differentiable-manifolds", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-af1407eeb0ee625d01eebae2" }, { "concept_id": "urn:uuid:a0553dab-d811-417e-8a79-67ec620792e7", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-15/01-differentiable-manifolds", "anchor": "first-00aa8b52b61298eda3c9-en", "chapter": "15", "section": "15.1", "offset": 7045, "range": [ 11726, 11968 ], "source_revision": "58a929d9614544dcb09f559c095b13f0f0ddf79dd34179c3ad56942fb79a9123", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "differentiable manifold", "context": { "range": [ 10936, 12001 ], "quote": "Any atlas $\\boldsymbol { A }$ may thus be extended to a maximal atlas by adding to it all charts that are $C ^ { \\infty }$ -compatible with the charts of . This maximal atlas is called a differentiable structure on $M$. 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