real analysis - Does there exist any continuous bijection between [0,1] and (0,1) and between [0,1] and IR?

We know that there are bijections between $[0,1]$, $(0,1)$ and $\mathbb{R}$. But my question is can we obtain a continuous bijection between $[0,1]$ and $(0,1)$, and between $[0,1]$ and $\mathbb{R}$?
I think there will not exist but I am not sure.