Last Updated
：2025/11/28
upper set
Noun
Japanese Meaning
上集合：順序集合において、ある要素を含むと、その要素以上の全ての要素（昇順に並ぶ要素）も含む部分集合。 / 上位集合：順序関係において、各要素に対して、その要素の上位に位置する全ての要素を含む部分集合。
（ plural ）
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(mathematics, order theory) A subset of a poset which contains any ascending chain which starts at any element of itself.
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upper set
In the poset, the subset U is an upper set because every ascending chain that starts at an element of U remains entirely within U.
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In the poset, the subset U is an upper set because every ascending chain that starts at an element of U remains entirely within U.
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