Hello,

I'm trying to do this problem

"Prove that if is a submanifold of a manifold , then is a submanifold of "

what I've thought so far is following:

Let be charts of . Since is a submanifold of , can be covered by a collection of with the property ( is the dimension of ). Let , I think I have to prove that can be covered by the collection of with the property

Could anyone give me suggestions or comments?