See distinguished open set in All languages combined, or Wiktionary
Download JSON data for distinguished open set meaning in English (2.3kB)
{
"forms": [
{
"form": "distinguished open sets",
"tags": [
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"expansion": "distinguished open set (plural distinguished open sets)",
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"pos": "noun",
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"name": "English entries with incorrect language header",
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"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Algebraic geometry",
"orig": "en:Algebraic geometry",
"parents": [
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"Geometry",
"Mathematics",
"Formal sciences",
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"glosses": [
"A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
],
"id": "en-distinguished_open_set-en-noun-1zlFDW5w",
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[
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[
"compliment",
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[
"hypersurface",
"hypersurface"
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[
"algebraic varieties",
"algebraic varieties"
],
[
"affine schemes",
"affine schemes"
],
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"projective",
"projective variety"
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"zero locus",
"zero locus"
],
[
"affine",
"affine space"
],
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"projective",
"projective space"
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"scheme theory"
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[
"prime ideal",
"prime ideal"
],
[
"commutative ring",
"commutative ring"
],
[
"element",
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],
"raw_glosses": [
"(algebraic geometry) A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
],
"topics": [
"algebraic-geometry",
"geometry",
"mathematics",
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]
}
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"word": "distinguished open set"
}
{
"forms": [
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"pos": "noun",
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{
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"glosses": [
"A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
],
"links": [
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"algebraic geometry",
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"set",
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"affine",
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"raw_glosses": [
"(algebraic geometry) A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring."
],
"topics": [
"algebraic-geometry",
"geometry",
"mathematics",
"sciences"
]
}
],
"word": "distinguished open set"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-15 from the enwiktionary dump dated 2024-05-02 using wiktextract (8203a16 and 304864d). 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.