There's a theorem that says any nested sequence of compact sets in Rn always has a non-empty intersection. So there is something wrong with this counterexample. I'm not able to see what's wrong:(adsbygoogle = window.adsbygoogle || []).push({});

Consider the interval Un = [2-1/n, 1+1/n] for n=1, 2 and 3.

Isn't the intersection of U1, U2 and U3 the null set? (since U3 is the null set?)

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# Nested sequence of compact sets in Rn has a non-empty intersection?

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