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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 Neat submanifold ： ウィキペディア英語版 Neat submanifold In differential topology, an area of mathematics, a neat submanifold of a manifold with boundary is a kind of "well-behaved" submanifold. More precisely, let $M$ be a manifold with boundary, and $A$ a submanifold of $M$. A is said to be a neat submanifold of $M$ if it meets the following two conditions:〔.〕 *The boundary of the submanifold coincides with the parts of the submanifold that are part of the boundary of the larger manifold. That is, $\backslash partial\; A\; =\; A\; \backslash cap\; \backslash partial\; M$. *Each point of the submanifold has a neighborhood within which the submanifold's embedding is equivalent to the embedding of a hyperplane in a higher-dimensional Euclidean space. More formally, $A$ must be covered by charts $(U,\; \backslash phi)$ of $M$ such that $A\; \backslash cap\; U\; =\; \backslash phi^(\backslash mathbb^m)$ where $m$ is the dimension For instance, in the category of smooth manifolds, this means that the embedding of $A$ must also be smooth. ==See also== *Local flatness 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「Neat submanifold」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.