The main result given in Theorem 1.1 is a condition for a map X, defined on the complement of a disk D in R2 with values in ℝ2, to be extended to a topological embedding of ℝ2, not necessarily surjective. The map X is supposed to be just differentiable with the condition that, for some ε > 0, at each point the eigenvalues of the differential do not belong to the real interval (-ε,∞). The extension is obtained by restricting X to the complement of some larger disc. The result has important connections with the property of asymptotic stability at infinity for differentiable vector fields. © Springer-Verlag Berlin Heidelberg 2006.