Answer to Question #133636 in Functional Analysis for PRATHIBHA ROSE C S

Question #133636
Suppose that (xalpha)alpha element of j converges to x in X and (yalpha)alpha element of j converges to y in Y .show that (xalpha×yalpha) converges to x × y in X×Y
1
Expert's answer
2020-09-23T16:06:42-0400

Let's suppose that "X" is a set with element "x" and that "Y" is a set with element "y". If we multiply two sets "X\u00d7Y", all their elements will be in this new set. And if elements "x" and "y" converge in sets "X" and "Y" respectively, their product "x\u00d7y" will converge in the set "X\u00d7Y". Q.E.D.


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