Hello,

I have a exercise, but the exercise isn't written very well. Do you understand, what the statement should be?:

"M is a smooth submanifold of N iff every point $\displaystyle p \in M$ has an open nbh $\displaystyle U_p \subset N$ , s.t. $\displaystyle U_p \cap M$ is a smooth submanifold of U".

It doesn't make sense to me, because p is a point in M and U_p a subset in N. And what about the set U?

Our definition of a submanifold: M is a submanifold of N if there exist a smooth embedding and immersion f:M-> N

thank you