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

Monday, April 30, 2018

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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