"disjoint union" meaning in All languages combined

See disjoint union on Wiktionary

Noun [English]

Forms: disjoint unions [plural]
Head templates: {{en-noun}} disjoint union (plural disjoint unions)
  1. (mathematics) A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing). Categories (topical): Mathematics, Category theory, Set theory Synonyms (union of sets forced to be disjoint): discriminated union Translations (union of sets forced to be disjoint): unione disgiunta [feminine] (Italian), disjunkt union (Swedish)
    Sense id: en-disjoint_union-en-noun-RsZSwq3O Disambiguation of Category theory: 22 38 40 Disambiguation of Set theory: 27 32 40 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Terms with Icelandic translations, Terms with Italian translations, Terms with Swedish translations Disambiguation of English entries with incorrect language header: 25 37 39 Disambiguation of Pages with 1 entry: 26 34 40 Disambiguation of Pages with entries: 26 35 39 Disambiguation of Terms with Icelandic translations: 24 38 38 Disambiguation of Terms with Italian translations: 22 43 35 Disambiguation of Terms with Swedish translations: 24 38 38 Topics: mathematics, sciences Disambiguation of 'union of sets forced to be disjoint': 46 35 19 Disambiguation of 'union of sets forced to be disjoint': 46 35 19
  2. (mathematics) A union of sets which are already pairwise disjoint. Categories (topical): Mathematics, Category theory, Set theory
    Sense id: en-disjoint_union-en-noun-VaFQCulz Disambiguation of Category theory: 22 38 40 Disambiguation of Set theory: 27 32 40 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Icelandic translations, Terms with Italian translations, Terms with Swedish translations Disambiguation of English entries with incorrect language header: 25 37 39 Disambiguation of Entries with translation boxes: 19 53 28 Disambiguation of Pages with 1 entry: 26 34 40 Disambiguation of Pages with entries: 26 35 39 Disambiguation of Terms with Icelandic translations: 24 38 38 Disambiguation of Terms with Italian translations: 22 43 35 Disambiguation of Terms with Swedish translations: 24 38 38 Topics: mathematics, sciences
  3. (topology) The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology. Categories (topical): Topology, Category theory, Set theory Synonyms (union of topological spaces equipped with a topology): coproduct, direct sum, free sum, free union, topological sum Translations (union of topologies): sundurlæga sammengi [neuter] (Icelandic)
    Sense id: en-disjoint_union-en-noun-td2xY1g6 Disambiguation of Category theory: 22 38 40 Disambiguation of Set theory: 27 32 40 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Terms with Icelandic translations, Terms with Italian translations, Terms with Swedish translations Disambiguation of English entries with incorrect language header: 25 37 39 Disambiguation of Pages with 1 entry: 26 34 40 Disambiguation of Pages with entries: 26 35 39 Disambiguation of Terms with Icelandic translations: 24 38 38 Disambiguation of Terms with Italian translations: 22 43 35 Disambiguation of Terms with Swedish translations: 24 38 38 Topics: mathematics, sciences, topology Disambiguation of 'union of topological spaces equipped with a topology': 15 20 65 Disambiguation of 'union of topologies': 25 33 42
The following are not (yet) sense-disambiguated
Synonyms (union of already disjoint sets): discriminated union Derived forms: disjoint union topology Related terms: coproduct, disjunctive union, product topology Translations (union of already disjoint sets): unione disgiunta [feminine] (Italian), disjunkt union (Swedish)
Disambiguation of 'union of already disjoint sets': 27 40 33 Disambiguation of 'union of already disjoint sets': 27 40 33

Inflected forms

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    {
      "_dis1": "29 38 33",
      "word": "disjoint union topology"
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  ],
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    {
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  "head_templates": [
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      "expansion": "disjoint union (plural disjoint unions)",
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  "pos": "noun",
  "related": [
    {
      "_dis1": "29 38 33",
      "word": "coproduct"
    },
    {
      "_dis1": "29 38 33",
      "word": "disjunctive union"
    },
    {
      "_dis1": "29 38 33",
      "word": "product topology"
    }
  ],
  "senses": [
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          "kind": "topical",
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            "Sciences",
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            "Fundamental"
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        {
          "_dis": "25 37 39",
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          "parents": [
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          "_dis": "26 34 40",
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          "_dis": "24 38 38",
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          "_dis": "22 38 40",
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          "_dis": "27 32 40",
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      ],
      "glosses": [
        "A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing)."
      ],
      "id": "en-disjoint_union-en-noun-RsZSwq3O",
      "links": [
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      "raw_glosses": [
        "(mathematics) A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing)."
      ],
      "synonyms": [
        {
          "_dis1": "46 35 19",
          "sense": "union of sets forced to be disjoint",
          "word": "discriminated union"
        }
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      "translations": [
        {
          "_dis1": "46 35 19",
          "code": "it",
          "lang": "Italian",
          "sense": "union of sets forced to be disjoint",
          "tags": [
            "feminine"
          ],
          "word": "unione disgiunta"
        },
        {
          "_dis1": "46 35 19",
          "code": "sv",
          "lang": "Swedish",
          "sense": "union of sets forced to be disjoint",
          "word": "disjunkt union"
        }
      ]
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          "_dis": "25 37 39",
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        {
          "_dis": "19 53 28",
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          "_dis": "26 34 40",
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          "_dis": "27 32 40",
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          "name": "Set theory",
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      "glosses": [
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      "id": "en-disjoint_union-en-noun-VaFQCulz",
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        "(mathematics) A union of sets which are already pairwise disjoint."
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          "_dis": "24 38 38",
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          "_dis": "22 38 40",
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          "_dis": "27 32 40",
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      "glosses": [
        "The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology."
      ],
      "id": "en-disjoint_union-en-noun-td2xY1g6",
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      "raw_glosses": [
        "(topology) The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology."
      ],
      "synonyms": [
        {
          "_dis1": "15 20 65",
          "sense": "union of topological spaces equipped with a topology",
          "word": "coproduct"
        },
        {
          "_dis1": "15 20 65",
          "sense": "union of topological spaces equipped with a topology",
          "word": "direct sum"
        },
        {
          "_dis1": "15 20 65",
          "sense": "union of topological spaces equipped with a topology",
          "word": "free sum"
        },
        {
          "_dis1": "15 20 65",
          "sense": "union of topological spaces equipped with a topology",
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          "_dis1": "15 20 65",
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      "translations": [
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          "_dis1": "25 33 42",
          "code": "is",
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          "sense": "union of topologies",
          "tags": [
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          ],
          "word": "sundurlæga sammengi"
        }
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      "_dis1": "27 40 33",
      "sense": "union of already disjoint sets",
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      "_dis1": "27 40 33",
      "code": "it",
      "lang": "Italian",
      "sense": "union of already disjoint sets",
      "tags": [
        "feminine"
      ],
      "word": "unione disgiunta"
    },
    {
      "_dis1": "27 40 33",
      "code": "sv",
      "lang": "Swedish",
      "sense": "union of already disjoint sets",
      "word": "disjunkt union"
    }
  ],
  "wikipedia": [
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  ],
  "word": "disjoint union"
}
{
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    "Pages with entries",
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      "word": "coproduct"
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    {
      "word": "product topology"
    }
  ],
  "senses": [
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        "en:Mathematics"
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      "glosses": [
        "A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing)."
      ],
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        "(mathematics) A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing)."
      ],
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        "sciences"
      ]
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      ],
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        "(topology) The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology."
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      "sense": "union of sets forced to be disjoint",
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    {
      "sense": "union of already disjoint sets",
      "word": "discriminated union"
    },
    {
      "sense": "union of topological spaces equipped with a topology",
      "word": "coproduct"
    },
    {
      "sense": "union of topological spaces equipped with a topology",
      "word": "direct sum"
    },
    {
      "sense": "union of topological spaces equipped with a topology",
      "word": "free sum"
    },
    {
      "sense": "union of topological spaces equipped with a topology",
      "word": "free union"
    },
    {
      "sense": "union of topological spaces equipped with a topology",
      "word": "topological sum"
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    {
      "code": "it",
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      "sense": "union of sets forced to be disjoint",
      "tags": [
        "feminine"
      ],
      "word": "unione disgiunta"
    },
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      "code": "sv",
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      "sense": "union of sets forced to be disjoint",
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    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "union of already disjoint sets",
      "tags": [
        "feminine"
      ],
      "word": "unione disgiunta"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "union of already disjoint sets",
      "word": "disjunkt union"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "union of topologies",
      "tags": [
        "neuter"
      ],
      "word": "sundurlæga sammengi"
    }
  ],
  "wikipedia": [
    "disjoint union"
  ],
  "word": "disjoint union"
}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.