I3

Q4. ) Let U be an open subset of R". We say that a k-form w on U is closed on U if dw = 0 on U. A k-form on U is said to be exact on U if there exists a (k - 1)-form n on U such that w = dn. Prove that every exact form on U is closed on U. Is every closed form on U exact on U? If yes, give a proof. If no, give a counterexample