C^infty question

1. Nov 13, 2005

Palindrom

Suppose h and h o f are both C^infty on f(U) and U correspondingly, with U an open set. Assume now that f(U) is open. Is f C^infty on U? Does anyone have a counter example?

I've edited the question so that it would actually make sense.

Last edited: Nov 13, 2005
2. Nov 13, 2005

mathwonk

trivially false. take h constant.

3. Nov 13, 2005

Palindrom

How very stupid of me. Thank you.