Theorem 2.36 says that given a collection of compact subsets of a metric space X such that the intersection of every finite subcollection is nonempty, then the intersection of the entire collection is nonempty. The proof is very simple and I easily follow the abstract reasoning. However, I think that there is a deeper intuition behind this example which I cannot quite seem to figure out.(adsbygoogle = window.adsbygoogle || []).push({});

Could anyone provide a more concrete explanation as to why it is the property of compactness that results in this property?

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# Baby rudin theorem 2.36 explanation

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