general topology - Continuous bijection from $mathbb{R}^{2} to mathbb{R}$

Can anyone give an example of a continuous bijection from $\mathbb{R}^{2} \to \mathbb{R}$

Answer

Ok, I will add my hint as an answer so that it's not unanswered.

• Not possible is my guess. If you remove finitely many points from $\mathbb R^2$ it remains connected where as $\mathbb R$ does not. That should be a hint.