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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 Upper topology ： ウィキペディア英語版 Upper topology In mathematics, the upper topology on a partially ordered set ''X'' is the coarsest topology in which the closure of a singleton $\backslash$ is the order section $a]=\backslash$ for each $a\backslash in\; X$. If $\backslash leq$ is a partial order, the upper topology is the least order consistent topology in which the open sets are the up-sets. The lower topology induced by the preorder is defined similarly in terms of the down-sets. The preoder inducing the upper topology is its specialization preorder, but the specialization preorder of the lower topology is opposite to the inducing preorder. The real upper topology is most naturally defined on the upper-extended real line $]-\backslash infty,+\backslash infty]=\backslash mathbb\backslash cup\backslash$ by the system $\backslash \backslash \}$ of open sets. Similarly, the real lower topology $\backslash \{\}$. ==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「Upper topology」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.