1) A vector form of Green's theorem states that under certain conditions, where n is the unit outward normal to the curve C and D is the region enclosed by C [Now, my question is: must n be a unit vector? Why or why not?] 2) A "regular region" is a compact set S in Rn that is the closure of its interior. Equivalently, a compact set S in Rn is a regular region if every neighborhood of every point on the boundary of S contains points in the interior of S [I don't understand at all why these are equivalent. Can somebody please explain?] Thanks a lot!