Saturday, 4 October 2014

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 R. But my question is can we obtain a continuous bijection between [0,1] and (0,1), and between [0,1] and R?
I think there will not exist but I am not sure.

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