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

[doggie_Walkes]

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).