See partially ordered set in All languages combined, or Wiktionary
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Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28,\nA partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of \"≻\" and speak of the partially ordered set P.\nThe ordered fields defined earlier are easily seen to be examples of partially ordered sets." }, { "ref": "1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35:", "text": "In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.", "type": "quote" }, { "ref": "2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45:", "text": "The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).", "type": "quote" } ], "glosses": [ "The ordered pair comprising a set and its partial order." ], "id": "en-partially_ordered_set-en-noun-8zd~fBuI", "links": [ [ "set theory", "set theory" ], [ "ordered pair", "ordered pair" ] ], "raw_glosses": [ "(set theory, order theory, formally) The ordered pair comprising a set and its partial order." ], "tags": [ "formal" ], "topics": [ "mathematics", "order-theory", "sciences", "set-theory" ] } ], "synonyms": [ { "_dis1": "52 48", "sense": "set on which a partial order is defined", "word": "ground set" }, { "_dis1": "52 48", "sense": "set on which a partial order is defined", "word": "poset" }, { "_dis1": "45 55", "sense": "ordered pair of set and partial order", "word": "poset" }, { "_dis1": "50 50", "source": "Thesaurus:partially ordered set", "word": "partially ordered set" } ], "translations": [ { "_dis1": "52 48", "code": "ar", "english": "Arabic Academy term", "lang": "Arabic", "roman": "fiʔatun murattabatun juzʔiyyan", "sense": "set having a specified partial order", "tags": [ "feminine" ], "word": "فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا" }, { "_dis1": "52 48", "code": "ar", "lang": "Arabic", "raw_tags": [ "in educational communities" ], "roman": "majmūʕatun murattabatun juzʔiyyan", "sense": "set having a specified partial order", "tags": [ "common", "feminine" ], "word": "مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا" }, { "_dis1": "52 48", "code": "cs", "lang": "Czech", "sense": "set having a specified partial order", "tags": [ "feminine" ], "word": "uspořádaná množina" }, { "_dis1": "52 48", "code": "fi", "lang": "Finnish", "sense": "set having a specified partial order", "word": "osittain järjestetty joukko" }, { "_dis1": "52 48", "code": "de", "lang": "German", "sense": "set having a specified partial order", "tags": [ "feminine" ], "word": "partiell geordnete Menge" }, { "_dis1": "52 48", "alt": "はんじゅんじょしゅうごう", "code": "ja", "lang": "Japanese", "roman": "hanjunjo-shūgō", "sense": "set having a specified partial order", "word": "半順序集合" }, { "_dis1": "52 48", "code": "sv", "lang": "Swedish", "sense": "set having a specified partial order", "tags": [ "common-gender" ], "word": "partiellt ordnad mängd" } ], "wikipedia": [ "partially ordered set" ], "word": "partially ordered set" }
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