I know that there does not exist a continuos function from [0,1] onto (0,1) because the image of a compact set for a continous function f must be compact, but isn't it also the case that the inverse image of a compact set must be compact? and a set in R is compact iff its closed and bounded right?(adsbygoogle = window.adsbygoogle || []).push({});

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# Continuous function from (0,1) onto [0,1]?

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