Search results with tag "Differentiable viewpoint"

TOPOLOGY FROM DIFFERENTIABLE VIEWPOINT

6 51. Smooth maniJolds smooth map f:M+N with f(x) = y.The derivative dfz : TM, 3 TN, is defined as follows.Since J is smooth there exist an open set W con- taining x and a smooth map F:W4R1 that coincides with f on W (7 M. De&e df,(v) to be equal to dF,(v) for all v e TM,. To justify this definition we must prove that dF,(v) belongs to TN, and that it does not depend on the …

  Viewpoint, Differentiable, Differentiable viewpoint