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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4$\begingroup$ $(0,1) $? ${}{}{} $ $\endgroup$– cqfdJan 1, 2020 at 9:09
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$\begingroup$ Any bounded open interval in $\mathbb R$ will do(for the usual topology). $\endgroup$– Sarvesh Ravichandran IyerJan 1, 2020 at 9:11
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1$\begingroup$ @астонвіллаолофмэллбэрг Thank you $\endgroup$– user738585Jan 1, 2020 at 9:14
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1$\begingroup$ @ThomasShelby thanks $\endgroup$– user738585Jan 1, 2020 at 9:14
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1$\begingroup$ @астонвіллаолофмэллбэрг Please post this as an answer, so that question can go off the unanswered question queue. $\endgroup$– ComFreekJan 1, 2020 at 9:34
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1 Answer
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In $\Bbb R$, usual topology, $(0,1)$ (or any bounded open interval) is precompact but not compact.
answered Jan 1, 2020 at 10:41