I think the definition and motivation of (sequential or open cover) compactness is somewhat unintuitive for beginners. I can find several good discussions on compactness here in math.stackexchange.com. I read them and they were very helpful. However, the compactness is still not so tangible to me. I think it would be helpful if there is a collection of "use cases" of compactness showing its power or usefulness. They could be proofs of some useful theorems involving compact sets or solutions of problems in applied maths or science/engineering. Thank you in advance.
2026-04-07 09:25:34.1775553934
Pedagogical use cases of compactness
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