Past exam of the metric spaces and complex analysis course of the University of Oxford / 2014 / 2 / b

For coordinate differences $a,b$, the elementary inequalitiesgiveThe identity map between the two versions of the square is bijective, and both it and its inverse are Lipschitz continuous maps by these inequalities. It is therefore a homeomorphism. In fact the same comparison works on all of ${\mathbb{R}}^2$; restriction to the square causes no difficulty.