Continuity and limits
Not what you're looking for? Search our solutions OR ask your own Custom question.
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)
© BrainMass Inc. brainmass.com December 24, 2021, 5:12 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/continuity-limits-points-35011
Solution Preview
Please see the attachment.
1. Proof:
Since is continuous, then for any and any neighborhood . We can find a neighborhood , such that . Similarly, since , for any and any ...
Solution Summary
This is a proof regarding continuity and products.
$2.49