See disjoint union on Wiktionary
Download JSON data for disjoint union meaning in All languages combined (6.0kB)
{
"derived": [
{
"_dis1": "29 38 33",
"word": "disjoint union topology"
}
],
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{
"form": "disjoint unions",
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"lang_code": "en",
"pos": "noun",
"related": [
{
"_dis1": "29 38 33",
"word": "coproduct"
},
{
"_dis1": "29 38 33",
"word": "disjunctive union"
},
{
"_dis1": "29 38 33",
"word": "product topology"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
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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": [
[
"mathematics",
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[
"union",
"union"
],
[
"set",
"set"
]
],
"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": "47 35 19",
"sense": "union of sets forced to be disjoint",
"word": "discriminated union"
}
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "47 35 19",
"code": "it",
"lang": "Italian",
"sense": "union of sets forced to be disjoint",
"tags": [
"feminine"
],
"word": "unione disgiunta"
},
{
"_dis1": "47 35 19",
"code": "sv",
"lang": "Swedish",
"sense": "union of sets forced to be disjoint",
"word": "disjunkt union"
}
]
},
{
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{
"_dis": "27 33 40",
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],
"glosses": [
"A union of sets which are already pairwise disjoint."
],
"id": "en-disjoint_union-en-noun-VaFQCulz",
"links": [
[
"mathematics",
"mathematics"
]
],
"raw_glosses": [
"(mathematics) A union of sets which are already pairwise disjoint."
],
"synonyms": [
{
"_dis1": "28 41 32",
"sense": "union of already disjoint sets",
"word": "discriminated union"
}
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "28 41 32",
"code": "it",
"lang": "Italian",
"sense": "union of already disjoint sets",
"tags": [
"feminine"
],
"word": "unione disgiunta"
},
{
"_dis1": "28 41 32",
"code": "sv",
"lang": "Swedish",
"sense": "union of already disjoint sets",
"word": "disjunkt union"
}
]
},
{
"categories": [
{
"kind": "topical",
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"name": "Topology",
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{
"_dis": "23 27 50",
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"name": "Category theory",
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{
"_dis": "27 33 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",
"links": [
[
"topology",
"topology"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(topology) The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology."
],
"synonyms": [
{
"_dis1": "13 17 70",
"sense": "union of topological spaces equipped with a topology",
"word": "coproduct"
},
{
"_dis1": "13 17 70",
"sense": "union of topological spaces equipped with a topology",
"word": "direct sum"
},
{
"_dis1": "13 17 70",
"sense": "union of topological spaces equipped with a topology",
"word": "free sum"
},
{
"_dis1": "13 17 70",
"sense": "union of topological spaces equipped with a topology",
"word": "free union"
},
{
"_dis1": "13 17 70",
"sense": "union of topological spaces equipped with a topology",
"word": "topological sum"
}
],
"topics": [
"mathematics",
"sciences",
"topology"
],
"translations": [
{
"_dis1": "25 32 43",
"code": "is",
"lang": "Icelandic",
"sense": "union of topologies",
"tags": [
"neuter"
],
"word": "sundurlæga sammengi"
}
]
}
],
"wikipedia": [
"disjoint union"
],
"word": "disjoint union"
}
{
"categories": [
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"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"en:Category theory",
"en:Set theory"
],
"derived": [
{
"word": "disjoint union topology"
}
],
"forms": [
{
"form": "disjoint unions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
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"expansion": "disjoint union (plural disjoint unions)",
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],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "coproduct"
},
{
"word": "disjunctive union"
},
{
"word": "product topology"
}
],
"senses": [
{
"categories": [
"en:Mathematics"
],
"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)."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"union",
"union"
],
[
"set",
"set"
]
],
"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)."
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Mathematics"
],
"glosses": [
"A union of sets which are already pairwise disjoint."
],
"links": [
[
"mathematics",
"mathematics"
]
],
"raw_glosses": [
"(mathematics) A union of sets which are already pairwise disjoint."
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Topology"
],
"glosses": [
"The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology."
],
"links": [
[
"topology",
"topology"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(topology) The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology."
],
"topics": [
"mathematics",
"sciences",
"topology"
]
}
],
"synonyms": [
{
"sense": "union of sets forced to be disjoint",
"word": "discriminated union"
},
{
"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"
}
],
"translations": [
{
"code": "it",
"lang": "Italian",
"sense": "union of sets forced to be disjoint",
"tags": [
"feminine"
],
"word": "unione disgiunta"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "union of sets forced to be disjoint",
"word": "disjunkt union"
},
{
"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"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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.
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