Upper set (original) (raw)
Horní množina a dolní množina jsou matematické pojmy z oboru teorie množin, konkrétněji z teorie uspořádání, které formalizují představu množiny, která obsahuje „s každým svým prvkem i všechny menší“ (dolní množina), resp. „s každým svým prvkem i všechny větší“ (horní množina).
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| dbo:abstract | Horní množina a dolní množina jsou matematické pojmy z oboru teorie množin, konkrétněji z teorie uspořádání, které formalizují představu množiny, která obsahuje „s každým svým prvkem i všechny menší“ (dolní množina), resp. „s každým svým prvkem i všechny větší“ (horní množina). (cs) En matemáticas, sección final (también llamado sección final abierta) de un conjunto parcialmente ordenado (X,≤) es un subconjunto U con la propiedad tal que, si x está en U y x≤y, entonces y está en U. La idea dual sería el sección inicial (alternativamente, conjunto decreciente, segmento inicial, semi-ideal; el conjunto es un sección inicial cerrada), el cual es un subconjunto L con la propiedad tal que, si x está en L y y≤x, entonces y está en L. Los términos orden ideal o se usan normalmente como sinónimos para referirse a la sección inicial. La elección de esta terminología no refleja la noción del ideal del retículo porque un conjunto inferior de un retículo no es necesariamente un sub retículo. (es) In matematica si definisce segmento iniziale (o taglio iniziale, o sottoinsieme chiuso verso il basso) di un dato insieme totalmente ordinato un qualsiasi suo sottoinsieme tale che: Il nome deriva abbastanza naturalmente dalla "forma" che un tale insieme ha: segmento perché non ha "buchi" - se sono in , ogni elemento tra e sarà in - iniziale perché contiene gli elementi di più piccoli. Casi particolari di segmenti iniziali di un insieme sono stesso e l'insieme vuoto. Simmetricamente, si definisce un segmento finale (o taglio finale, o sottoinsieme chiuso verso l'alto) mediante la proprietà Gli insiemi degli interi negativi e positivi sono rispettivamente un segmento iniziale e un segmento finale di (it) En mathématiques, et plus précisément en théorie des ordres, une section commençante (également appelée segment initial ou sous-ensemble fermé inférieurement) d'un ensemble ordonné (X,≤) est un sous-ensemble S de X tel que si x est dans S et si y ≤ x, alors y est dans S. Dualement, on appelle section finissante (ou sous-ensemble fermé supérieurement) un sous-ensemble F tel que si x est dans F et si x ≤ y, alors y est dans F. (fr) In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set is a subset with the following property: if s is in S and if x in X is larger than s (that is, if ), then x is in S. In words, this means that any x element of X that is to some element of S is necessarily also an element of S. The term lower set (also called a downward closed set, down set, decreasing set, initial segment, or semi-ideal) is defined similarly as being a subset S of X with the property that any element x of X that is to some element of S is necessarily also an element of S. (en) ( 상집합(商集合)에 대해서는 몫집합 문서를 참고하십시오.) 순서론에서 상집합(上集合, 영어: upper set, upward-closed set, upset)은 에 속하는 원소보다 더 큰 임의의 원소 역시 에 속하는, 원순서 집합의 부분 집합 이다. 마찬가지로, 하집합(下集合, 영어: lower set, downward-closed set, downset)은 에 속하는 원소보다 더 작은 임의의 원소 역시 에 속하는, 원순서 집합의 부분 집합 이다. (ko) Em matemática, mais precisamente em teoria da ordem, um segmento inicial de um conjunto ordenado (X,≤) é um subconjunto S de X tal que se x pertence à S e se y≤x, então y pertence à S. (pt) 在数学中，上部集合（向上闭合集合）是给定偏序集合 (X,≤) 的子集 Y，使得对于所有元素 x 和 y，如果 x 小于等于 y，并且 x 是 Y 的一个元素，则 y 也在 Y 中。更加形式的说 概念是下部集合(向下闭合集合)，它是给定偏序集合 (X,≤) 的任何子集 Y，使得对于所有元素 x 和 y，如果 x 小于等于 y，并且 y 是 Y 的一个元素，则 x 也在 Y 中。更加形式的说 (zh) Верхня множина (замкнена вверх множина) — підмножина частково впорядкованої множини , яка задовольняє умову: Двоїстим поняттям є — нижня множина. (uk) |
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| dbo:wikiPageExternalLink | http://www-compsci.swan.ac.uk/~csjens/pdf/top.pdf%7Cdoi=10.1016/s0304-3975(99)00045-6%7Cdoi-access=free https://web.archive.org/web/20070621125416/http:/www.mathematik.tu-darmstadt.de:8080/Math-Net/Lehrveranstaltungen/Lehrmaterial/SS2003/Topology/separation.pdf |
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| rdfs:comment | Horní množina a dolní množina jsou matematické pojmy z oboru teorie množin, konkrétněji z teorie uspořádání, které formalizují představu množiny, která obsahuje „s každým svým prvkem i všechny menší“ (dolní množina), resp. „s každým svým prvkem i všechny větší“ (horní množina). (cs) En mathématiques, et plus précisément en théorie des ordres, une section commençante (également appelée segment initial ou sous-ensemble fermé inférieurement) d'un ensemble ordonné (X,≤) est un sous-ensemble S de X tel que si x est dans S et si y ≤ x, alors y est dans S. Dualement, on appelle section finissante (ou sous-ensemble fermé supérieurement) un sous-ensemble F tel que si x est dans F et si x ≤ y, alors y est dans F. (fr) In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set is a subset with the following property: if s is in S and if x in X is larger than s (that is, if ), then x is in S. In words, this means that any x element of X that is to some element of S is necessarily also an element of S. The term lower set (also called a downward closed set, down set, decreasing set, initial segment, or semi-ideal) is defined similarly as being a subset S of X with the property that any element x of X that is to some element of S is necessarily also an element of S. (en) ( 상집합(商集合)에 대해서는 몫집합 문서를 참고하십시오.) 순서론에서 상집합(上集合, 영어: upper set, upward-closed set, upset)은 에 속하는 원소보다 더 큰 임의의 원소 역시 에 속하는, 원순서 집합의 부분 집합 이다. 마찬가지로, 하집합(下集合, 영어: lower set, downward-closed set, downset)은 에 속하는 원소보다 더 작은 임의의 원소 역시 에 속하는, 원순서 집합의 부분 집합 이다. (ko) Em matemática, mais precisamente em teoria da ordem, um segmento inicial de um conjunto ordenado (X,≤) é um subconjunto S de X tal que se x pertence à S e se y≤x, então y pertence à S. (pt) 在数学中，上部集合（向上闭合集合）是给定偏序集合 (X,≤) 的子集 Y，使得对于所有元素 x 和 y，如果 x 小于等于 y，并且 x 是 Y 的一个元素，则 y 也在 Y 中。更加形式的说 概念是下部集合(向下闭合集合)，它是给定偏序集合 (X,≤) 的任何子集 Y，使得对于所有元素 x 和 y，如果 x 小于等于 y，并且 y 是 Y 的一个元素，则 x 也在 Y 中。更加形式的说 (zh) Верхня множина (замкнена вверх множина) — підмножина частково впорядкованої множини , яка задовольняє умову: Двоїстим поняттям є — нижня множина. (uk) En matemáticas, sección final (también llamado sección final abierta) de un conjunto parcialmente ordenado (X,≤) es un subconjunto U con la propiedad tal que, si x está en U y x≤y, entonces y está en U. La idea dual sería el sección inicial (alternativamente, conjunto decreciente, segmento inicial, semi-ideal; el conjunto es un sección inicial cerrada), el cual es un subconjunto L con la propiedad tal que, si x está en L y y≤x, entonces y está en L. (es) In matematica si definisce segmento iniziale (o taglio iniziale, o sottoinsieme chiuso verso il basso) di un dato insieme totalmente ordinato un qualsiasi suo sottoinsieme tale che: Il nome deriva abbastanza naturalmente dalla "forma" che un tale insieme ha: segmento perché non ha "buchi" - se sono in , ogni elemento tra e sarà in - iniziale perché contiene gli elementi di più piccoli. Casi particolari di segmenti iniziali di un insieme sono stesso e l'insieme vuoto. Gli insiemi degli interi negativi e positivi sono rispettivamente un segmento iniziale e un segmento finale di (it) |
| rdfs:label | Dolní a horní množina (cs) Sección final (es) Section commençante (fr) Segmento iniziale (it) 상집합 (ko) Segmento inicial (matemática) (pt) Upper set (en) Верхня множина (uk) 上闭集合 (zh) |
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