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Saw this in the thread about "Explaining topology..."

Is there an easy way to extend this particular definition to when f : R^n -> R^m?matt grime said:in R^n f is differentaible at x if there is a linaer map Df(x) satisfying

f(x+h)=f(x)+Df(x)h + ho(|h|)

this can be extended to any place where there is a notion of linear map or a map such as |?| to the reals, or some other ordered space.

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