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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 Disjunction property of Wallman ： ウィキペディア英語版 Disjunction property of Wallman In mathematics, especially in order theory, a partially ordered set with a unique minimal element 0 has the disjunction property of Wallman when for every pair (''a'', ''b'') of elements of the poset, either ''b'' ≤ ''a'' or there exists an element ''c'' ≤ ''b'' such that ''c'' ≠ 0 and ''c'' has no nontrivial common predecessor with ''a''. That is, in the latter case, the only ''x'' with ''x'' ≤ ''a'' and ''x'' ≤ ''c'' is ''x'' = 0. A version of this property for lattices was introduced by , in a paper showing that the homology theory of a topological space could be defined in terms of its distributive lattice of closed sets. He observed that the inclusion order on the closed sets of a T1 space has the disjunction property. The generalization to partial orders was introduced by . ==References== *. *. 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「Disjunction property of Wallman」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.