Show that f can be uniformly approximated on X by polynomials in x ad in y with real coefficients.

(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.

(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**).