See differentiable manifold in All languages combined, or Wiktionary
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Pontryagin, Characteristic Cycles on Differentiable Manifolds, American Mathematical Society, page 33:", "text": "Whitney showed that a differentiable manifold Mᵏ can be regularly mapped on the vector space R#x7B;2k#x7D;.", "type": "quote" }, { "ref": "1994, N. Aoki, K. Hiraide, Topological Theory of Dynamical Systems: Recent Advances, Elsevier (North-Holland), page 1:", "text": "The phase space of a dynamical system will be taken to be a differentiable manifold.", "type": "quote" }, { "ref": "2009, Jeffrey Marc Lee, Manifolds and Differential Geometry, American Mathematical Society, page 1:", "text": "In this chapter we introduce differentiable manifolds and smooth maps. A differentiable manifold' is a topological space on which there are defined coordinates allowing basic notions of differentiability.", "type": "quote" } ], "glosses": [ "A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;" ], "id": "en-differentiable_manifold-en-noun-iocL7SnK", "links": [ [ "differential geometry", "differential geometry" ], [ "manifold", "manifold" ], [ "locally", "locally" ], [ "Euclidean space", "Euclidean space" ], [ "calculus", "calculus" ], [ "atlas", "atlas" ], [ "chart", "chart" ] ], "qualifier": "differential geometry", "raw_glosses": [ "(differential geometry) A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Differential geometry", "orig": "en:Differential geometry", "parents": [ "Geometry", "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "30 70", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "28 72", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "12 88", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "20 80", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "23 77", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "18 82", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "25 75", "kind": "other", "langcode": "en", "name": "Manifolds", "orig": "en:Manifolds", "parents": [], "source": "w+disamb" } ], "glosses": [ "A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;\n(more formally) a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).", "a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts)." ], "id": "en-differentiable_manifold-en-noun-wARJzdpl", "links": [ [ "differential geometry", "differential geometry" ], [ "manifold", "manifold" ], [ "locally", "locally" ], [ "Euclidean space", "Euclidean space" ], [ "calculus", "calculus" ], [ "atlas", "atlas" ], [ "chart", "chart" ] ], "qualifier": "differential geometry; more formally", "raw_glosses": [ "(differential geometry) A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;" ], "synonyms": [ { "_dis1": "43 57", "word": "differential manifold" } ] } ], "translations": [ { "_dis1": "50 50", "code": "fr", "lang": "French", "sense": "manifold locally similar enough to a Euclidean space for calculus to be done", "tags": [ "feminine" ], "word": "variété différentiable" }, { "_dis1": "50 50", "code": "fr", "lang": "French", "sense": "manifold locally similar enough to a Euclidean space for calculus to be done", "tags": [ "feminine" ], "word": "variété différentielle" }, { "_dis1": "50 50", "code": "de", "lang": "German", "sense": "manifold locally similar enough to a Euclidean space for calculus to be done", "tags": [ "feminine" ], "word": "differenzierbare Mannigfaltigkeit" }, { "_dis1": "50 50", "code": "it", "lang": "Italian", "sense": "manifold locally similar enough to a Euclidean space for calculus to be done", "tags": [ "feminine" ], "word": "varietà differenziabile" } ], "wikipedia": [ "differentiable manifold" ], "word": "differentiable manifold" }
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