Tight span of subsets of the plane with the maximum metric

Abstract

We prove that a nonempty closed and geodesically convex subset of the l(infinity) plane R-infinity(2) is hyperconvex and we characterize the tight spans of arbitrary subsets of R-infinity(2) via this property: Given any nonempty X subset of R-infinity(2), a closed, geodesically convex and minimal subset Y subset of R-infinity(2) containing X is isometric to the tight span T(X) of X