Let C_b(R) denote the space of all bounded, continuous functions f : Let C_0(R) denote the set of continuous functions f : R C for which lim x f(x) =...

 Let C_b(R) denote the space of all bounded, continuous functions f : R → C. Let C_0(R) denote the set of continuous functions f : R → C for which lim x→±∞ f(x) = 0. How do you prove that C_b(R) and C_0(R) are complete in the uniform metric?