5 Let X and X′ denote a single set in the topologies  respectively; let Y and Y′ denote a...

5 Let X and X′ denote a single set in the topologies  respectively; let Y and Y′ denote a single set in the topologies  respectively. Assume these sets are nonempty.

(a) Show that if  and , then the product topology on X′ × Y′ is finer than the product topology on X × Y.

(b) Does the converse of (a) hold? Justify your answer.