Deduce the same results for v x0 z0 by applying theorem

Question

This exercise develops an alternative proof of Theorem 16.3.

(a) Choose the appropriate topology on Z so that U is continuous on X × X × Z.

(b) Use Theorem A.12 in Appendix A to show that the objective function in Problem 16.1 is continuous in the product topology; Theorem A.13 and Lemma A.2 to show that the constraint set is compact; and Theorems A.9 and A.16 to show that V∗(x(0), z(0)) is well defined, continuous, and bounded over X × Z.

(c) Deduce the same results for V (x(0), z(0)) by applying Theorem 16.1.