"coordinate map" meaning in English

{
  "forms": [
    {
      "form": "coordinate maps",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "coordinate map (plural coordinate maps)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Differential geometry",
          "orig": "en:Differential geometry",
          "parents": [
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Functions",
          "orig": "en:Functions",
          "parents": [
            "Algebra",
            "Calculus",
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2019 January 2, John M. Lee, Introduction to Riemannian Manifolds (Graduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 135:",
          "text": "Let (W#x5F;0,#x5C;psi) be a smooth coordinate chart for P, and let (E#x5F;1,#x5C;dots,E#x5F;#x7B;n-p#x7D;) be a local orthonormal frame for the normal bundle NP; by shrinking W#x5F;0 if necessary, we can assume that the coordinates and the local frame are defined on the same open subset W#x5F;0#x5C;subseteqP. Let #x5C;hat#x7B;W#x7D;#x5F;0#x3D;#x5C;psi(W#x5F;0)#x5C;subseteq#x5C;mathbb#x7B;R#x7D;ᵖ, and let NP#x5C;vert#x5F;#x7B;W#x5F;0#x7D; be the portion of the normal bundle over W#x5F;0. The coordinate map #x5C;psi and frame (E#x5F;j) yield a diffeomorphism #x5C;hat#x7B;W#x7D;#x5F;0#x5C;times#x5C;mathbb#x7B;R#x7D;#x7B;n-p#x7D;#x5C;rightarrowNP#x5C;vert#x5F;#x7B;W#x5F;0#x7D; defined by[…]",
          "type": "quote"
        }
      ],
      "glosses": [
        "Synonym of coordinate chart."
      ],
      "id": "en-coordinate_map-en-noun-PLvhI9oZ",
      "links": [
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "coordinate chart",
          "coordinate chart#English"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) Synonym of coordinate chart."
      ],
      "synonyms": [
        {
          "tags": [
            "synonym",
            "synonym-of"
          ],
          "word": "coordinate chart"
        }
      ]
    }
  ],
  "word": "coordinate map"
}

{
  "forms": [
    {
      "form": "coordinate maps",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "coordinate map (plural coordinate maps)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Differential geometry",
        "en:Functions"
      ],
      "examples": [
        {
          "ref": "2019 January 2, John M. Lee, Introduction to Riemannian Manifolds (Graduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 135:",
          "text": "Let (W#x5F;0,#x5C;psi) be a smooth coordinate chart for P, and let (E#x5F;1,#x5C;dots,E#x5F;#x7B;n-p#x7D;) be a local orthonormal frame for the normal bundle NP; by shrinking W#x5F;0 if necessary, we can assume that the coordinates and the local frame are defined on the same open subset W#x5F;0#x5C;subseteqP. Let #x5C;hat#x7B;W#x7D;#x5F;0#x3D;#x5C;psi(W#x5F;0)#x5C;subseteq#x5C;mathbb#x7B;R#x7D;ᵖ, and let NP#x5C;vert#x5F;#x7B;W#x5F;0#x7D; be the portion of the normal bundle over W#x5F;0. The coordinate map #x5C;psi and frame (E#x5F;j) yield a diffeomorphism #x5C;hat#x7B;W#x7D;#x5F;0#x5C;times#x5C;mathbb#x7B;R#x7D;#x7B;n-p#x7D;#x5C;rightarrowNP#x5C;vert#x5F;#x7B;W#x5F;0#x7D; defined by[…]",
          "type": "quote"
        }
      ],
      "glosses": [
        "Synonym of coordinate chart."
      ],
      "links": [
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "coordinate chart",
          "coordinate chart#English"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) Synonym of coordinate chart."
      ],
      "synonyms": [
        {
          "tags": [
            "synonym",
            "synonym-of"
          ],
          "word": "coordinate chart"
        }
      ]
    }
  ],
  "word": "coordinate map"
}