Everywhere I have looked from the internet to books to my college notes I have not been able to find any fully worked solutions to showing more abstract sets are compact. It's obvious sets like (0,1] are not compact but what about more difficult sets like the set of bounded non-decreasing functions with the supremum metric ? Could anyone please link me to some pages that go through in detail how to solve more difficult problems like that ? I find it so much easier to learn by looking at completed proofs and trying to follow the logic!
2026-03-29 02:36:22.1774751782
Please, where can I find some good worked examples of compact spaces?
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You can try looking here: https://en.wikipedia.org/wiki/Counterexamples_in_Topology. And in any handbook on general topology, very often after section about "paracompactness" or "completeness" or sth connected to compactness there are some counterexamples. If you are looking after non compact function spaces, then you can try "$C_p$ theory problem book" by Tkachuk.