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smooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold.
==Definition==
A smooth structure on a manifold ''M'' is a collection of smoothly equivalent smooth atlases. Here, a smooth atlas for a topological manifold ''M'' is an atlas for ''M'' such that each transition function is a smooth map, and two smooth atlases for ''M'' are smoothly equivalent provided their union is again a smooth atlas for ''M''. This gives a natural equivalence relation on the set of smooth atlases.
A smooth manifold is a topological manifold ''M''
together with a smooth structure on ''M''.
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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