Compact convex sets in 2-dimensional asymmetric normed lattices

Abstract

In this note, we study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric description of the compact convex set with non empty interior in (R²; q), where q is an asymmetric lattice norm.

Keywords: Asymmetric norm, asymmetric lattice norm, compactness, convex body, convex sets