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.

Mathematics Subject Classification (2010):

• 46A50
• 46A55
• 46B50
• 52A07
• 52A10

Key words:

• Asymmetric norm
• asymmetric lattice norm
• compactness
• convex body
• convex sets