Consider two metric spaces (X, dx) and (Y, dy). Show that if | X| is finite, then there does not exist a function f : X Y that is continuous. Prove that given metric spaces (X, dx), (Y, dy), (Z, dz), if : X Y is contiu- ous at xo and g: Y Z is continuous at f(xo), then the composite function gof: X Z is continuous at xo.