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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 Submanifold ： ウィキペディア英語版 Submanifold In mathematics, a submanifold of a manifold ''M'' is a subset ''S'' which itself has the structure of a manifold, and for which the inclusion map ''S'' → ''M'' satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. ==Formal definition== In the following we assume all manifolds are differentiable manifolds of class ''C''''r'' for a fixed ''r'' ≥ 1, and all morphisms are differentiable of class ''C''''r''. 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「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.