(1) Assume that converges uniformly to on and that each is uniformly continuous on . Prove that is uniformly continuous on
(2) Assume converges uniformly to on a compact set , and let be a continuous function on satisfying . Show converges uniformly on to
(3) Assume and are uniformly convergent sequences of functions.
(a) Show that is a uniformly convergent sequence of functions.
(b)Give an example to show that the product may not converge uniformly.
(c) Prove that if there exists an such that and for all , then does converge uniformly.
I need a walkthrough with these, thanks