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

1. Jan 3, 2010

### doggie_Walkes

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

2. Jan 4, 2010

### rochfor1

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

3. Jan 4, 2010

### 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).