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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 Fixed-point space ： ウィキペディア英語版 Fixed-point space In mathematics, a Hausdorff space ''X'' is called a fixed-point space if every continuous function $f:X\backslash rightarrow\; X$ has a fixed point. For example, any closed interval () in $\backslash mathbb\; R$ is a fixed point space, and it can be proved from the intermediate value property of real continuous function. The open interval (''a'', ''b''), however, is not a fixed point space. To see it, consider the function $f(x)\; =\; a\; +\; \backslash frac\backslash cdot(x-a)^2$, for example. Any linearly ordered space that is connected and has a top and a bottom element is a fixed point space. Note that, in the definition, we could easily have disposed of the condition that the space is Hausdorff. ==References== * Vasile I. Istratescu, ''Fixed Point Theory, An Introduction'', D. Reidel, the Netherlands (1981). ISBN 90-277-1224-7 * Andrzej Granas and James Dugundji, ''Fixed Point Theory'' (2003) Springer-Verlag, New York, ISBN 0-387-00173-5 * William A. Kirk and Brailey Sims, ''Handbook of Metric Fixed Point Theory'' (2001), Kluwer Academic, London ISBN 0-7923-7073-2 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「Fixed-point 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.