Definition
Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both
and its inverse
are differentiable (if these functions are r times continuously differentiable, f is called a -diffeomorphism).
Two manifolds M and N are diffeomorphic (symbol usually being ) if there is a smooth bijective map f from M to N with a smooth inverse. They are diffeomorphic if there is an r times continuously differentiable bijective map between them whose inverse is also r times continuously differentiable.
Read more about this topic: Diffeomorphism
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