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# Continuity and limits

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1. For i = 1,2 let fi: Xi --> Yi be maps between topological spaces. Show that the product f1Xf2: X1XX2 --> Y1XY2 defined by f1Xf2(x1x2):= (f1(x1), f2(x2)) is continuous if and only if f1 and f2 are continuous.

*(Please see attachment for proper representation of formulas and problem #2)

https://brainmass.com/math/real-analysis/continuity-limits-points-35011