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.
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