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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 Stein manifold ： ウィキペディア英語版 Stein manifold In the theory of several complex variables and complex manifolds in mathematics, a Stein manifold is a complex submanifold of the vector space of ''n'' complex dimensions. They were introduced by and named after . A Stein space is similar to a Stein manifold but is allowed to have singularities. Stein spaces are the analogues of affine varieties or affine schemes in algebraic geometry. == Definition == A complex manifold $X$ of complex dimension $n$ is called a Stein manifold if the following conditions hold: * $X$ is holomorphically convex, i.e. for every compact subset $K\; \backslash subset\; X$, the so-called ''holomorphic convex hull'', ::$\backslash bar\; K\; =\; \backslash ,$ :is again a ''compact'' subset of $X$. Here $\backslash mathcal\; O(X)$ denotes the ring of holomorphic functions on $X$. * $X$ is holomorphically separable, i.e. if $x\; \backslash neq\; y$ are two points in $X$, then there is a holomorphic function ::$f\; \backslash in\; \backslash mathcal\; O(X)$ :such that $f(x)\; \backslash neq\; f(y).$ 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「Stein manifold」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.