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Timeline for Being contained in a compact set

Current License: CC BY-SA 4.0

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Jun 15, 2023 at 8:08 history edited Taras Banakh CC BY-SA 4.0
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Jun 15, 2023 at 6:04 comment added Taras Banakh @Arno You are right this example separates (1) and (2). So now the problem is to separate (2) and (3), or prove that they are equivalent (at least under some separation axioms).
Jun 15, 2023 at 5:37 vote accept Arno
Jun 15, 2023 at 5:37 comment added Arno If I'm not missing something, the example already separates Properties (1) and (2) - any sequence in $A$ should have a converging subsequence, too. (And the space is a great example in many other ways, thanks!)
Jun 14, 2023 at 21:20 comment added Taras Banakh @Wojowu Thank you for the comment. I added more details to my answer. Is it Ok now?
Jun 14, 2023 at 21:20 history edited Taras Banakh CC BY-SA 4.0
Added more details
Jun 14, 2023 at 21:09 comment added Wojowu I imagine you take this hedgehog as your $\mathcal X$, what would your $A$ be?
Jun 14, 2023 at 20:46 history answered Taras Banakh CC BY-SA 4.0