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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）』
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