TITLE: Whitney embedding for manifolds with boundary
QUESTION [7 upvotes]: Suppose one has a smooth manifold with boundary M and compact on top of it. Is it true that it can always be embedded in an upper half plane such that the boundary is embedded in the hiperplane $x_n=0$? Or are there obstructions to that? If yes, what are those obstructions? Thank you!

REPLY [5 votes]: See  Theorem 1.4.3. of

M. Hirsch: Differential Topology, Springer Verlag, 1976