I'm trying to solve Exercise 15.12 from Lee's Introduction to Smooth Manifolds which says "Suppose M is an oriented smooth manifold with or without boundary, and $D\subset M$ is a smooth codimension-$0$ submanifold with or without boundary. Then the orientation of M restricts to an orientation of D. "
My initial attempt was just to restrict the orientable charts of M to N, and that seemed to work but I don't see why we need the codimension to be $0$. Is there something I'm missing here?