# Quick Question about Smooth Maps

slevvio
Hello everyone, I just had a quick question I was hoping somebody could answer.

If $f: M \times N \rightarrow P$ is a smooth map, where $M,N$ and $P$ are smooth manifolds, then is it true for fixed $m$ that $f_m : N \rightarrow P$ is smooth, where $f_m (n) = f(m,n)$?

Any help would be appreciated.

## Answers and Replies

Science Advisor
Homework Helper
Gold Member
Of course, since the equivalent statement when M=R^m, N=R^n is true.

slevvio
ok thank you!