- #1
jecharla
- 24
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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.
Could anyone provide a more concrete explanation as to why it is the property of compactness that results in this property?
Could anyone provide a more concrete explanation as to why it is the property of compactness that results in this property?