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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 Banach bundle (non-commutative geometry) ： ウィキペディア英語版 Banach bundle (non-commutative geometry) In mathematics, a Banach bundle is a fiber bundle over a topological Hausdorff space, such that each fiber has the structure of a Banach space. == Definition == Let $X$ be a topological Hausdorff space, a (continuous) Banach bundle over $X$ is a tuple $\backslash mathfrak\; =\; (B,\; \backslash pi)$, where $B$ is a topological Hausdorff space, and $\backslash pi\backslash colon\; B\backslash to\; X$ is a continuous, open surjection, such that each fiber $B\_x\; :=\; \backslash pi^(x)$ is a Banach space. Which satisfies the following conditions: # The map $b\backslash mapsto\backslash |b\backslash |$ is continuous for all $b\backslash in\; B$ # The operation $+\backslash colon\backslash \backslash to\; B$ is continuous # For every $\backslash lambda\backslash in\backslash mathbb$, the map $b\backslash mapsto\backslash lambda\backslash cdot\; b$ is continuous # If $x\backslash in\; X$, and $\backslash$ is a net in $B$, such that $\backslash |b\_i\backslash |\backslash to\; 0$ and $\backslash pi(b\_i)\backslash to\; x$, then $b\_i\backslash to\; 0\_x\backslash in\; B$. Where $0\_x$ denotes the zero of the fiber $B\_x$.〔Fell, M.G., Doran, R.S.: "Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 1"〕 If the map $b\backslash mapsto\; \backslash |b\backslash |$ is only upper semi-continuous, $\backslash mathfrak$ is called upper semi-continuous bundle. 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「Banach bundle (non-commutative geometry)」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.