Why does the set have to be (bounded) and closed in order for there being finitely many open subsets that can completely cover it?(adsbygoogle = window.adsbygoogle || []).push({});

My question is concerned with the closed aspect (I know why it has to be bounded). So why can't a bounded and open set be able to be covered by finitely many open subsets?

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# Heine-Borel Theorem

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