(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that it is not necessarily true that the infinite union of closed sets is closed

2. Relevant equations

3. The attempt at a solution

From intuition, I came up with the following counter-example: ##\displaystyle \bigcup_{n=2}^{\infty} \left[ \frac{1}{n}, \frac{n}{n+1} \right] = (0,1)##. However, I am not sure how to actuallyprovethat this infintie union is the set on the right. How would I do so?

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# Homework Help: Infinite union of closed sets is not closed

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