I have seen a few questions about this but still don’t understand. Why is it that for infinitely many open sets their intersection might not necessarily be open?
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1Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Jun 07 '22 at 11:37
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1Look at $\bigcap_{n\ge1}(-1/n,1/n)$. – Kenta S Jun 07 '22 at 11:39
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1$\bigcap_{n\in\mathbb{N}}(a-1/n,a+1/n)={a}$ – jcneek Jun 07 '22 at 11:39