Prove that countable intersections of closed subset of R^d are closed

doggie_Walkes

rochfor1

Try proving that countable unions of open subsets of R^d are open.

JSuarez

If the intersection is not empty (what happens if it is?), consider a convergent sequence x(n) in it; what must happen to the limit? (Remember that closed sets must contain the limits of their convergent sequences).

Similar Threads for: Prove that countable intersections of closed subset of R^d are closed
Thread	Forum	Replies
Metric Space, closed ball is a closed set. prove this	Calculus & Beyond Homework	5
Closed subset of XxY?	Calculus & Beyond Homework	4
Prove that if C and D are closed sets, then C U D is a closed set.	Calculus & Beyond Homework	8
Proving that a certian subset of L^1([0,1]) is closed	Calculus & Beyond Homework	2

doggie_Walkes	Prove that countable intersections of closed subset of R^d are closed Tweet Prove that countable intersections of closed subset of R^d are closed

rochfor1	Try proving that countable unions of open subsets of R^d are open.

JSuarez	If the intersection is not empty (what happens if it is?), consider a convergent sequence x(n) in it; what must happen to the limit? (Remember that closed sets must contain the limits of their convergent sequences).