Saturday, November 25, 2017

real analysis - Whether there is a continuous bijection from $(0,1)$ to closed interval $[0,1]$.

Is there a continuous bijection from open interval $(0,1)$ to $[0,1]$. The answer is not. How to prove?



I think it may proceed by contradiction and apply open mapping theorem. However, $(0,1)$ is not complete. I get stuck.

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