Global injectivity conditions for planar maps

We prove that a planar $C^1$ -smooth map $f:Dlongrightarrow mathbb{R }^{2n}$ , where $Dsubseteq mathbb{R }^{2n}$ is a convex open set, is injective if $mathbb{R }cap mathrm{Spec}(df)_z=emptyset $ for all $zin D$ . We continue by showing that the triangulability of the differentials $(df)_z$ , $zin D$ , ensure the global injectivity as well.