Differentiable Functions On Manifolds
See also: Differentiable manifold#Differentiable functionsIf M is a differentiable manifold, a real or complex-valued function ƒ on M is said to be differentiable at a point p if it is differentiable with respect to some (or any) coordinate chart defined around p. More generally, if M and N are differentiable manifolds, a function ƒ: M → N is said to be differentiable at a point p if it is differentiable with respect to some (or any) coordinate charts defined around p and ƒ(p).
Read more about this topic: Local Linearity
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