Munkres... Ah, the memories... (actually never went deeper than page 4)

Take . Then the closed unit ball of H^n.

We check , h in (tangent space). Since this generates an n-1 dimensional subspace - alternatively, because its kernel is only the zero vector - df(x) has rank 1 at all points of M.

So N is an n-dimensional manifold, and its boundary is E^{n-1} - of dimension n-1.