# Closed sets in C

1. Jan 24, 2012

### autre

1. The problem statement, all variables and given/known data

Show by example that an infinite union of closed sets in $\mathbb{C}$ need not be closed.

3. The attempt at a solution

In $\mathbb{R}$ I know that an infinite union of the closed sets $A_{n}=[1/n,1-1/n]$ is open. Not sure if it works in $\mathbb{C}$ as well.

2. Jan 24, 2012

### SammyS

Staff Emeritus
Try closed balls, or closed rectangles.