Let X and X' denote a single set in the topologies T and T', respectively; let Y and Y' denote a single set in the topologies U and U', respectively. Assume these sets are nonempty.

(i) show that if T'$\displaystyle \supset$T and U'$\displaystyle \supset$U, then the product topology on X' x Y' is finer than the product topology on X x Y.

(ii) does the converse of (i) hold? And how would I justify this