"differentiable manifold" meaning in All languages combined

{
  "forms": [
    {
      "form": "differentiable manifolds",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "differentiable manifold (plural differentiable manifolds)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "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": "46 54",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "49 51",
          "kind": "other",
          "langcode": "en",
          "name": "Manifolds",
          "orig": "en:Manifolds",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "text": "The charts (homeomorphisms) that make up any differentiable structure of a differentiable manifold are required to be such that the transition from one to another is differentiable.",
          "type": "example"
        },
        {
          "ref": "1950, L. S. 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": "quotation"
        },
        {
          "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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 is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;"
      ],
      "id": "en-differentiable_manifold-en-noun-hD0CqNcu",
      "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;\n"
      ]
    },
    {
      "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": "46 54",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "49 51",
          "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;\n"
      ]
    }
  ],
  "synonyms": [
    {
      "_dis1": "50 50",
      "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"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "en:Manifolds"
  ],
  "forms": [
    {
      "form": "differentiable manifolds",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "differentiable manifold (plural differentiable manifolds)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "English terms with usage examples",
        "en:Differential geometry"
      ],
      "examples": [
        {
          "text": "The charts (homeomorphisms) that make up any differentiable structure of a differentiable manifold are required to be such that the transition from one to another is differentiable.",
          "type": "example"
        },
        {
          "ref": "1950, L. S. 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": "quotation"
        },
        {
          "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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 is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;"
      ],
      "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;\n"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "English terms with usage examples",
        "en:Differential geometry"
      ],
      "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)."
      ],
      "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;\n"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "differential manifold"
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "manifold locally similar enough to a Euclidean space for calculus to be done",
      "tags": [
        "feminine"
      ],
      "word": "variété différentiable"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "manifold locally similar enough to a Euclidean space for calculus to be done",
      "tags": [
        "feminine"
      ],
      "word": "variété différentielle"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "manifold locally similar enough to a Euclidean space for calculus to be done",
      "tags": [
        "feminine"
      ],
      "word": "differenzierbare Mannigfaltigkeit"
    },
    {
      "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"
}