Tuesday 20 December 2016

analysis - Is there a continuous function from $[0, 1]$ onto $(0, 1)$?




If there is none, why?



And for the other side, what about open set $(0, 1)$ to closed set $[0, 1]$ with a continuous function?



Thanks


Answer



HINT: For the first one use the fact that, Continuous image of a compact set is compact.


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