real analysis - Can a function from $(0,1)$ to $(0,1]$ be one-to-one and onto?

Sunday, February 25, 2018

real analysis - Can a function from $(0,1)$ to $(0,1]$ be one-to-one and onto?

Does there exist a function from $(0,1)$ to $(0,1]$ both one-to-one and onto, not necessarily continuous?

I couldn't think of any. Any help would be appreciated!

Thanks,

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