"Lefschetz fixed-point theorem" meaning in English

See Lefschetz fixed-point theorem in All languages combined, or Wiktionary

Proper name

Forms: the Lefschetz fixed-point theorem [canonical]
Etymology: Named after Solomon Lefschetz, who first stated it in 1926. Head templates: {{en-proper noun|def=1}} the Lefschetz fixed-point theorem
  1. (mathematics) A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X. Wikipedia link: Lefschetz fixed-point theorem Categories (topical): Mathematics
    Sense id: en-Lefschetz_fixed-point_theorem-en-name-Dg4x2Ua6 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: mathematics, sciences
{
  "etymology_text": "Named after Solomon Lefschetz, who first stated it in 1926.",
  "forms": [
    {
      "form": "the Lefschetz fixed-point theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Lefschetz fixed-point theorem",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "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": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X."
      ],
      "id": "en-Lefschetz_fixed-point_theorem-en-name-Dg4x2Ua6",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "formula",
          "formula"
        ],
        [
          "fixed point",
          "fixed point"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "mapping",
          "mapping"
        ],
        [
          "compact",
          "compact"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "trace",
          "trace"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Lefschetz fixed-point theorem"
      ]
    }
  ],
  "word": "Lefschetz fixed-point theorem"
}
{
  "etymology_text": "Named after Solomon Lefschetz, who first stated it in 1926.",
  "forms": [
    {
      "form": "the Lefschetz fixed-point theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Lefschetz fixed-point theorem",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "formula",
          "formula"
        ],
        [
          "fixed point",
          "fixed point"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "mapping",
          "mapping"
        ],
        [
          "compact",
          "compact"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "trace",
          "trace"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Lefschetz fixed-point theorem"
      ]
    }
  ],
  "word": "Lefschetz fixed-point theorem"
}

Download raw JSONL data for Lefschetz fixed-point theorem meaning in English (1.3kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-02-12 from the enwiktionary dump dated 2025-02-02 using wiktextract (1c4b89b and 9dbd323). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.