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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 Bourbaki–Witt theorem ： ウィキペディア英語版 Bourbaki–Witt theorem In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed point theorem for partially ordered sets. It states that if ''X'' is a non-empty chain complete poset, and : $f\; :\; X\; \backslash to\; X$ such that : $f\; (x)\; \backslash geq\; x$ for all $x,$ then ''f'' has a fixed point. Such a function ''f'' is called ''inflationary'' or ''progressive''. == Special case of a finite poset == If the poset ''X'' is finite then the statement of the theorem has a clear interpretation that leads to the proof. The sequence of successive iterates, : $x\_=f(x\_n),\; n=0,1,2,\backslash ldots,$ where ''x''0 is any element of ''X'', is monotone increasing. By the finiteness of ''X'', it stabilizes: : $x\_n=x\_,\backslash quad$ for ''n'' sufficiently large. It follows that ''x''∞ is a fixed point of ''f''. 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「Bourbaki–Witt theorem」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.