# Proving question

1. Oct 2, 2005

### trap

I need help with this question which askes to prove it. Anyone has any idea?

If $$\text C_{1} , C_{2} , C_{3}$$ , … are all closed sets in $$\text R^n$$ , then the set $$\text c = I_{k=1}^{\infty}c_{k}$$ is also a closed set in $$\text R^n$$ .

2. Oct 2, 2005

What is I ?

3. Oct 2, 2005

### phoenixthoth

You want to show that the intersection contains all of its limit points. Try letting z be in cl(C), the closure of C, such that a sequence {z_n} in C converges to z. Then show that z must be in C.