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 topol

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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 Topol 1 (40.74 KiB) Viewed 33 times

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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. (a) Show that if T' )T and U' U, 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.