Union of Closed Sets: Finite vs. Infinite Examples

Bachelier · Apr 5, 2011

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 · Apr 5, 2011

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

Bachelier · Apr 5, 2011

Good. Thanks.

Union of Closed Sets: Finite vs. Infinite Examples

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Union of Closed Sets: Finite vs. Infinite Examples

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