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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 Biholomorphism ： ウィキペディア英語版 Biholomorphism In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic. ==Formal definition== Formally, a ''biholomorphic function'' is a function $\backslash phi$ defined on an open subset ''U'' of the $n$-dimensional complex space C''n'' with values in C''n'' which is holomorphic and one-to-one, such that its image is an open set $V$ in C''n'' and the inverse $\backslash phi^:V\backslash to\; U$ is also holomorphic. More generally, ''U'' and ''V'' can be complex manifolds. As in the case of functions of a single complex variable, a sufficient condition for a holomorphic map to be biholomorphic onto its image is that the map is injective, in which case the inverse is also holomorphic (e.g., see Gunning 1990, Theorem I.11). If there exists a biholomorphism $\backslash phi\; \backslash colon\; U\; \backslash to\; V$, we say that ''U'' and ''V'' are biholomorphically equivalent or that they are biholomorphic. 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「Biholomorphism」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.