If f from R to R is continuous, does it then follow that the pre-image of the closed unit interval [0,1] is compact?(adsbygoogle = window.adsbygoogle || []).push({});

-At first I thought of a counterexample like f=sinx but it seems that its range is not R. So will the answer be yes? And how can we prove it? Will the preimage have to be bounded in this case?

Thanks.

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# About the preimage of a compact set

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