"homotopy" meaning in All languages combined

See homotopy on Wiktionary

Noun [English]

Forms: homotopies [plural]
Etymology: From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs. Etymology templates: {{der|en|grc|ὁμός||same, similar}} Ancient Greek ὁμός (homós, “same, similar”), {{m|grc|τόπος||place}} τόπος (tópos, “place”) Head templates: {{en-noun|~}} homotopy (countable and uncountable, plural homotopies)
  1. (topology) A continuous deformation of one continuous function or map to another. Tags: countable, uncountable Categories (topical): Topology Hyponyms (continuous deformation): isotopy, regular homotopy Translations ((topology) continuous deformation of one continuous function to another): homotopi [common-gender] (Danish), homotopie [feminine] (French), ομοτοπία (omotopía) [feminine] (Greek), homotópia (Hungarian), samtogun [feminine] (Icelandic), ホモトピー (Japanese), 연속 변형 함수 (yeonsok byeonhyeong hamsu) (Korean), 호모토피 (homotopi) (Korean), هموتوپی (hemotopi) (Persian), homotopia [feminine] (Portuguese), homotopía [feminine] (Spanish), гомотопія (homotopija) [feminine] (Ukrainian), đồng luân (Vietnamese)
    Sense id: en-homotopy-en-noun-mk5aiw6X Topics: mathematics, sciences, topology Disambiguation of 'continuous deformation': 76 13 5 3 3 Disambiguation of '(topology) continuous deformation of one continuous function to another': 56 17 4 10 12
  2. (uncountable) The relationship between two continuous functions where homotopy from one to the other is evident. Tags: uncountable
    Sense id: en-homotopy-en-noun-YpP8NWnM
  3. (informal) Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes). Tags: abbreviation, alt-of, countable, ellipsis, informal, uncountable Alternative form of: homotopy theory (extra: the systematic study of homotopies and their equivalence classes)
    Sense id: en-homotopy-en-noun-s5Y-xV5B Categories (other): English links with redundant wikilinks, English entries with incorrect language header Disambiguation of English entries with incorrect language header: 4 29 47 14 6
  4. (topology) A theory associating a system of groups with each topological space. Tags: countable, uncountable Categories (topical): Topology
    Sense id: en-homotopy-en-noun-RZXyIvoX Topics: mathematics, sciences, topology
  5. (topology) A system of groups associated with a topological space. Tags: countable, uncountable Categories (topical): Topology Translations ((topology) system of groups associated with a topological space): homotopie [feminine] (French), homotópia (Hungarian), homotopía [feminine] (Spanish)
    Sense id: en-homotopy-en-noun-EfBp7ZeX Topics: mathematics, sciences, topology Disambiguation of '(topology) system of groups associated with a topological space': 5 1 4 38 52
The following are not (yet) sense-disambiguated
Related terms: homotopic, homeotopy group, homology Translations ((topology) theory associating a system of groups with each topological space): homotopie [feminine] (French), homotópia (Hungarian), homotopía [feminine] (Spanish)
Derived forms: cohomotopy, homotopic, homotopy category, homotopy class, homotopy equivalence, homotopy equivalent, homotopy fiber, homotopy fibre, homotopy group, homotopy invariant, homotopy relative to a subspace, homotopy theory, homotopy type, linear homotopy, regular homotopy, straight-line homotopy Disambiguation of '(topology) theory associating a system of groups with each topological space': 5 2 7 47 39

Inflected forms

Download JSON data for homotopy meaning in All languages combined (10.0kB)

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          "word": "연속 변형 함수"
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          "_dis1": "56 17 4 10 12",
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      ],
      "raw_glosses": [
        "(informal) Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes)."
      ],
      "tags": [
        "abbreviation",
        "alt-of",
        "countable",
        "ellipsis",
        "informal",
        "uncountable"
      ]
    },
    {
      "categories": [
        "en:Topology"
      ],
      "glosses": [
        "A theory associating a system of groups with each topological space."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "theory",
          "theory"
        ],
        [
          "group",
          "group"
        ],
        [
          "topological space",
          "topological space"
        ]
      ],
      "raw_glosses": [
        "(topology) A theory associating a system of groups with each topological space."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    },
    {
      "categories": [
        "en:Topology"
      ],
      "glosses": [
        "A system of groups associated with a topological space."
      ],
      "links": [
        [
          "topology",
          "topology"
        ]
      ],
      "raw_glosses": [
        "(topology) A system of groups associated with a topological space."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "translations": [
    {
      "code": "da",
      "lang": "Danish",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "common-gender"
      ],
      "word": "homotopi"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "feminine"
      ],
      "word": "homotopie"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "omotopía",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "feminine"
      ],
      "word": "ομοτοπία"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "word": "homotópia"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "feminine"
      ],
      "word": "samtogun"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "word": "ホモトピー"
    },
    {
      "code": "ko",
      "lang": "Korean",
      "roman": "yeonsok byeonhyeong hamsu",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "word": "연속 변형 함수"
    },
    {
      "code": "ko",
      "lang": "Korean",
      "roman": "homotopi",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "word": "호모토피"
    },
    {
      "code": "fa",
      "lang": "Persian",
      "roman": "hemotopi",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "word": "هموتوپی"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "feminine"
      ],
      "word": "homotopia"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "feminine"
      ],
      "word": "homotopía"
    },
    {
      "code": "uk",
      "lang": "Ukrainian",
      "roman": "homotopija",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "tags": [
        "feminine"
      ],
      "word": "гомотопія"
    },
    {
      "code": "vi",
      "lang": "Vietnamese",
      "sense": "(topology) continuous deformation of one continuous function to another",
      "word": "đồng luân"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "(topology) theory associating a system of groups with each topological space",
      "tags": [
        "feminine"
      ],
      "word": "homotopie"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "(topology) theory associating a system of groups with each topological space",
      "word": "homotópia"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "(topology) theory associating a system of groups with each topological space",
      "tags": [
        "feminine"
      ],
      "word": "homotopía"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "(topology) system of groups associated with a topological space",
      "tags": [
        "feminine"
      ],
      "word": "homotopie"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "(topology) system of groups associated with a topological space",
      "word": "homotópia"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "(topology) system of groups associated with a topological space",
      "tags": [
        "feminine"
      ],
      "word": "homotopía"
    }
  ],
  "wikipedia": [
    "Oswald Veblen",
    "homotopy"
  ],
  "word": "homotopy"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-04-26 from the enwiktionary dump dated 2024-04-21 using wiktextract (93a6c53 and 21a9316). 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.