Quote:
Originally Posted by jinydu
By definition of the boundary of a manifold, every point on the boundary has an open neighborhood that is diffeomorphic to R^{n1} x [0,infinity), which of course I can shrink to R^{n1} x [0,1).

(Thinking aloud here) Can you do said shrinking via a mapping which satisfies the same restrictions as the theta_i "basis functions" from the partition of unity theorem?