"vector bundle" meaning in English

{
  "forms": [
    {
      "form": "vector bundles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "vector bundle (plural vector bundles)",
      "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": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1995, Mauro Beltrametti, Andrew John Sommese, The Adjunction Theory of Complex Projective Varieties, Walter de Gruyter, page 8",
          "text": "Let E and F be two vector bundles on a compact algebraic set X.",
          "type": "quotation"
        },
        {
          "text": "2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5,\nThis solutions actually depend on the choice of a trivialisation ξ of the universal family 𝒫(n,d) of stable vector bundles of rank n and degree d."
        },
        {
          "ref": "2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130",
          "text": "Definition 6.1.5 A non-zero vector bundle #x5C;mathcal#x7B;F#x7D; on X is said to be decomposable if it can be written as #x5C;mathcal#x7B;F#x7D;#x5F;1#x5C;oplus#x5C;mathcal#x7B;F#x7D;#x5F;2 with #x5C;mathcal#x7B;F#x7D;#x5F;1 and #x5C;mathcal#x7B;F#x7D;#x5F;2 non-zero vector bundles. Otherwise it is said to be indecomposable.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A fiber bundle for which the fiber is a vector space."
      ],
      "hypernyms": [
        {
          "word": "fiber bundle"
        }
      ],
      "hyponyms": [
        {
          "word": "tangent bundle"
        }
      ],
      "id": "en-vector_bundle-en-noun-PWgoKX3C",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "category theory",
          "category theory"
        ],
        [
          "fiber bundle",
          "fiber bundle"
        ],
        [
          "fiber",
          "fiber"
        ],
        [
          "vector space",
          "vector space"
        ]
      ],
      "meronyms": [
        {
          "word": "zero section"
        }
      ],
      "raw_glosses": [
        "(topology, category theory) A fiber bundle for which the fiber is a vector space."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences",
        "topology"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "vektorikimppu"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Vektorbündel"
        }
      ],
      "wikipedia": [
        "vector bundle"
      ]
    }
  ],
  "word": "vector bundle"
}

{
  "forms": [
    {
      "form": "vector bundles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "vector bundle (plural vector bundles)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "fiber bundle"
    }
  ],
  "hyponyms": [
    {
      "word": "tangent bundle"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "word": "zero section"
    }
  ],
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Translation table header lacks gloss",
        "en:Category theory",
        "en:Topology"
      ],
      "examples": [
        {
          "ref": "1995, Mauro Beltrametti, Andrew John Sommese, The Adjunction Theory of Complex Projective Varieties, Walter de Gruyter, page 8",
          "text": "Let E and F be two vector bundles on a compact algebraic set X.",
          "type": "quotation"
        },
        {
          "text": "2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5,\nThis solutions actually depend on the choice of a trivialisation ξ of the universal family 𝒫(n,d) of stable vector bundles of rank n and degree d."
        },
        {
          "ref": "2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130",
          "text": "Definition 6.1.5 A non-zero vector bundle #x5C;mathcal#x7B;F#x7D; on X is said to be decomposable if it can be written as #x5C;mathcal#x7B;F#x7D;#x5F;1#x5C;oplus#x5C;mathcal#x7B;F#x7D;#x5F;2 with #x5C;mathcal#x7B;F#x7D;#x5F;1 and #x5C;mathcal#x7B;F#x7D;#x5F;2 non-zero vector bundles. Otherwise it is said to be indecomposable.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A fiber bundle for which the fiber is a vector space."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "category theory",
          "category theory"
        ],
        [
          "fiber bundle",
          "fiber bundle"
        ],
        [
          "fiber",
          "fiber"
        ],
        [
          "vector space",
          "vector space"
        ]
      ],
      "raw_glosses": [
        "(topology, category theory) A fiber bundle for which the fiber is a vector space."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "vector bundle"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "vektorikimppu"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Vektorbündel"
    }
  ],
  "word": "vector bundle"
}