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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Chain complete ： ウィキペディア英語版 Chain complete In order-theoretic mathematics, a partially ordered set is chain complete if every chain in it has a least upper bound. It is ω-complete when every increasing sequence of elements (a type of countable chain) has a least upper bound; the same notion can be extended to other cardinalities of chains.〔.〕 ==Examples== Every complete poset is chain complete. Unlike complete posets, chain complete posets are relatively common. Examples include: * The set of all linearly independent subsets of a vector space ''V'', ordered by inclusion. * The set of all partial functions on a set, ordered by restriction. * The set of all partial choice functions on a collection of non-empty sets, ordered by restriction. * The set of all prime ideals of a ring, ordered by inclusion. * The set of all consistent theories of a first-order language. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chain complete」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.