Union of Closed Sets: Finite vs. Infinite Examples

[Bachelier]

A Union of a FINITE collection of closed sets is closed. But if it is an infinite collection?
Can someone provide an example please?

 

[micromass]

The standard counterexample is this: \bigcup_{n\geq 1}{[1/n,1]}. This is a union of closed sets, but the union equals ]0,1] and this is not closed.

 

[Bachelier]

Good. Thanks.