Continuous surjective map Does there exist a continuous surjective map from $\{(x, y)\in \mathbb{R^2} | x^2-y^2=1\}$ to $\mathbb{R}$?
Any help would be greatly appreciated. I was trying to work with taking one branch of the hyperbola and restricting the function to it. But I cannot understand how to proceed much further.

Yes! Ascribe points of hyperbola with $x>0$ to positive numbers and points with $x<0$ to negative ones. Also map $(1,0)$ and $(-1,0)$ to 0.
