Hopf number in English

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{
  "forms": [
    {
      "form": "Hopf numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Hopf number (plural Hopf numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [],
          "source": "w"
        },
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        {
          "kind": "other",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "An integer-valued topological invariant that quantifies the linking of preimages in continuous maps from the 3-sphere to the 2-sphere."
      ],
      "id": "en-Hopf_number-en-noun-YUif1Ps6",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "valued",
          "valued"
        ],
        [
          "topological",
          "topological"
        ],
        [
          "invariant",
          "invariant"
        ],
        [
          "linking",
          "linking"
        ],
        [
          "preimage",
          "preimage"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "map",
          "map"
        ]
      ],
      "raw_glosses": [
        "(topology) An integer-valued topological invariant that quantifies the linking of preimages in continuous maps from the 3-sphere to the 2-sphere."
      ],
      "synonyms": [
        {
          "word": "Hopf invariant"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "Hopf number"
}

[Show JSON for raw wiktextract data ▼] [Hide JSON for raw wiktextract data ▲]

{
  "forms": [
    {
      "form": "Hopf numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Hopf number (plural Hopf numbers)",
      "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",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Topology"
      ],
      "glosses": [
        "An integer-valued topological invariant that quantifies the linking of preimages in continuous maps from the 3-sphere to the 2-sphere."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "valued",
          "valued"
        ],
        [
          "topological",
          "topological"
        ],
        [
          "invariant",
          "invariant"
        ],
        [
          "linking",
          "linking"
        ],
        [
          "preimage",
          "preimage"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "map",
          "map"
        ]
      ],
      "raw_glosses": [
        "(topology) An integer-valued topological invariant that quantifies the linking of preimages in continuous maps from the 3-sphere to the 2-sphere."
      ],
      "synonyms": [
        {
          "word": "Hopf invariant"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "Hopf number"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2026-06-15 from the enwiktionary dump dated 2026-06-01 using wiktextract (03da280 and 7f4db16). 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.

"Hopf number" meaning in English

Noun

Inflected forms