Question

Let X : = Πα∈IXα be a product space (with the product topology), πα : X → Xα be the projection map for each α∈I, and {xn}_{}^{}_{n=1}^{\infty } be a sequence in X. Prove that the sequence {xn} converges to a point x∈X if and only if {πα(xn)} converges to πα(x) for every α∈I.

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Ans Given x := IT Xx is a product space LEI To: X → X is the projection map for each LEI. Now {xnn is دن a sequence in X. LetAlow ki open nba for each Xi (@i 21,2,.. n) is an To(x) in Xa; by hypothesis { a (xn} converges to Mag(x) i=1,2,...,n ans in

Add a comment
Know the answer?
Add Answer to:
Let X : = Πα∈IXα be a product space (with the product topology), πα : X...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT