TOPOLOGY FROM DIFFERENTIABLE VIEWPOINT
Translating both hyperplanes to the origin, one obtains dfz. Before giving the actual definition, we must study the special case of mappings between open sets. For any open set U C Rk the tangent space TU, is defined to be the entire vector space Rk. For any smooth map f: U + V the derivatiue dfz ; Rk + R' is defined by the formula
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