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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 Noetherian space ： ウィキペディア英語版 Noetherian topological space In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the complements of the closed subsets. It can also be shown to be equivalent that every open subset of such a space is compact, and in fact the seemingly stronger statement that ''every'' subset is compact. == Definition == A topological space $X$ is called Noetherian if it satisfies the descending chain condition for closed subsets: for any sequence :$Y\_1\; \backslash supseteq\; Y\_2\; \backslash supseteq\; \backslash cdots$ of closed subsets $Y\_i$ of $X$, there is an integer $m$ such that $Y\_m=Y\_=\backslash cdots.$ 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「Noetherian topological space」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.