See preordered in All languages combined, or Wiktionary
{ "head_templates": [ { "args": { "1": "en", "2": "verb form" }, "expansion": "preordered", "name": "head" } ], "lang": "English", "lang_code": "en", "pos": "verb", "senses": [ { "form_of": [ { "word": "preorder" } ], "glosses": [ "simple past and past participle of preorder" ], "id": "en-preordered-en-verb-kSLWpCiL", "links": [ [ "preorder", "preorder#English" ] ], "tags": [ "form-of", "participle", "past" ] } ], "word": "preordered" } { "head_templates": [ { "args": { "1": "-" }, "expansion": "preordered (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Set theory", "orig": "en:Set theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "85 15", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "89 11", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "93 7", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1980, Johann Schröder, Operator Inequalities, Academic Press, page 8:", "text": "Most of the theory of this section on linear order spaces (and cones) can be generalized to preordered linear spaces (and wedges).", "type": "quote" }, { "ref": "1998, Ghanshyam B. Mehta, “Chapter 1: Preference and Utility”, in Salvador Barbera, Peter Hammond, Christian Seidl, editors, Handbook of Utility Theory, Volume 1: Principles, Springer, page 30:", "text": "It can be proved [see Herden (1989a,c, 1990, 1993a,b) and Herden and Mehta (1997a) that a continuous isotone (or strictly isotone) function defined on a closed subset K of a preordered topological space X has a continuous isotone (or strictly isotone) extension to a function g on X if and only if there is a separable system on X which satisfies certain \"separation\" conditions.", "type": "quote" }, { "ref": "1999, Rafael Villarroel-Flores, Equivariant Homotopy Type of Categories and Preordered Sets, University of Minnesota, page 24:", "text": "We remind the reader that the barycentric subdivision sd(P) of a preordered set P is the poset of chains in P, ordered by inclusion.", "type": "quote" } ], "glosses": [ "Equipped with a preorder." ], "id": "en-preordered-en-adj-IwJLV4Bd", "links": [ [ "set theory", "set theory" ], [ "preorder", "preorder" ] ], "raw_glosses": [ "(set theory, order theory, of a set) Equipped with a preorder." ], "raw_tags": [ "of a set" ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "order-theory", "sciences", "set-theory" ] } ], "word": "preordered" }
{ "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English non-lemma forms", "English uncomparable adjectives", "English verb forms", "Pages with 1 entry", "Pages with entries" ], "head_templates": [ { "args": { "1": "en", "2": "verb form" }, "expansion": "preordered", "name": "head" } ], "lang": "English", "lang_code": "en", "pos": "verb", "senses": [ { "form_of": [ { "word": "preorder" } ], "glosses": [ "simple past and past participle of preorder" ], "links": [ [ "preorder", "preorder#English" ] ], "tags": [ "form-of", "participle", "past" ] } ], "word": "preordered" } { "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English non-lemma forms", "English uncomparable adjectives", "English verb forms", "Pages with 1 entry", "Pages with entries" ], "head_templates": [ { "args": { "1": "-" }, "expansion": "preordered (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ "English terms with quotations", "en:Set theory" ], "examples": [ { "ref": "1980, Johann Schröder, Operator Inequalities, Academic Press, page 8:", "text": "Most of the theory of this section on linear order spaces (and cones) can be generalized to preordered linear spaces (and wedges).", "type": "quote" }, { "ref": "1998, Ghanshyam B. Mehta, “Chapter 1: Preference and Utility”, in Salvador Barbera, Peter Hammond, Christian Seidl, editors, Handbook of Utility Theory, Volume 1: Principles, Springer, page 30:", "text": "It can be proved [see Herden (1989a,c, 1990, 1993a,b) and Herden and Mehta (1997a) that a continuous isotone (or strictly isotone) function defined on a closed subset K of a preordered topological space X has a continuous isotone (or strictly isotone) extension to a function g on X if and only if there is a separable system on X which satisfies certain \"separation\" conditions.", "type": "quote" }, { "ref": "1999, Rafael Villarroel-Flores, Equivariant Homotopy Type of Categories and Preordered Sets, University of Minnesota, page 24:", "text": "We remind the reader that the barycentric subdivision sd(P) of a preordered set P is the poset of chains in P, ordered by inclusion.", "type": "quote" } ], "glosses": [ "Equipped with a preorder." ], "links": [ [ "set theory", "set theory" ], [ "preorder", "preorder" ] ], "raw_glosses": [ "(set theory, order theory, of a set) Equipped with a preorder." ], "raw_tags": [ "of a set" ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "order-theory", "sciences", "set-theory" ] } ], "word": "preordered" }
Download raw JSONL data for preordered meaning in English (2.5kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.