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.