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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 Tietze extension theorem ： ウィキペディア英語版 Tietze extension theorem In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary. ==Formal statement== If ''X'' is a normal topological space and :$f:\; A\; \backslash to\; \backslash mathbb$ is a continuous map from a closed subset ''A'' of ''X'' into the real numbers carrying the standard topology, then there exists a continuous map :$F:\; X\; \backslash to\; \backslash mathbb$ with ''F''(''a'') = ''f''(''a'') for all ''a'' in ''A''. Moreover, ''F'' may be chosen such that $\backslash sup\; \backslash \; =\; \backslash sup\; \backslash$, i.e., if ''f'' is bounded, ''F'' may be chosen to be bounded (with the same bound as ''f''). ''F'' is called a ''continuous extension'' 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「Tietze extension 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.