- #1

JonnyG

- 234

- 45

If I wanted to prove that a given function was smooth, are there any faster ways other than showing that its coordinate representation is smooth? For example, I just did a question where I had to show that ##T(M \times N)## is diffeomorphic to ##T(M) \times T(N)##. I had to explicitly construct a bijection between the two manifolds then show that the coordinate representations of ##F## and ##F^{-1}## were smooth. This was a big pain. I wish there was a theorem I could have appealed to instead.