Injective Convex Polyhedra

الأصل · EN

It was shown by Nachbin in 1950 that an n-dimensional normed space X is injective or equivalently is an absolute 1-Lipschitz retract if and only if X is linearly isometric to l∞ⁿ (i.e., Rⁿ endowed with the l∞-metric). We give an effective convex geometric characterization of injective convex polyhedra in l∞ⁿ. As an application, we prove that if the set of solutions to a linear system of inequalities with at most two variables per inequality is non-empty, then it is injective when endowed with the l∞-metric.