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I know that every compact set is precompact but not every precompact set is compact.I can't find an example of precompact set which is not compact .If you know can you enlighten me ?

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    $\begingroup$ $(0,1) $? ${}{}{} $ $\endgroup$
    – cqfd
    Jan 1, 2020 at 9:09
  • $\begingroup$ Any bounded open interval in $\mathbb R$ will do(for the usual topology). $\endgroup$ Jan 1, 2020 at 9:11
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    $\begingroup$ @астонвіллаолофмэллбэрг Thank you $\endgroup$
    – user738585
    Jan 1, 2020 at 9:14
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    $\begingroup$ @ThomasShelby thanks $\endgroup$
    – user738585
    Jan 1, 2020 at 9:14
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    $\begingroup$ @астонвіллаолофмэллбэрг Please post this as an answer, so that question can go off the unanswered question queue. $\endgroup$
    – ComFreek
    Jan 1, 2020 at 9:34

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In $\Bbb R$, usual topology, $(0,1)$ (or any bounded open interval) is precompact but not compact.

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