Closed Sets in \mathbb{C}: Showing Unclosedness by Example

[autre]

Homework Statement

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

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.

 

[SammyS]

Homework Statement

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

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.

Try closed balls, or closed rectangles.