Similar, let's see some work (you will clearly need to look at the complex version of the S.W.T)(2) Let X be the closed unit disc in the complex plane (denoted C).
Show that any function in C(X,C) can be uniformly approx on X by polynomials in z and conjugate z with complex coefficients.
Slightly trickier, ideas?(3) Let X and Y be compact Hausdorff spaces, and f a function in C(XxY,C).
Show that f can be uniformly approx. by functions of the form Sum(from 1 to n)(f_i)(g_i), where the f_i's are in C(X,C) and the g_i's are in C(Y,C).