Article

Compact convex sets in 2-dimensional asymmetric normed lattices

Published in: Quaestiones Mathematicae
Volume 39 , issue 1 , 2016 , pages: 73–82

DOI: 10.2989/16073606.2015.1023864

Author(s): Natalia Jonard-Pérez Departamento de Mateḿaticas, Spain , Enrique A. Sánchez-Pérez Instituto Universitario de Matéatica Pura y Aplicada, Universitat Polit̀ecnica de Val̀encia, Spain

Keywords: 46A50 , 46A55 , 46B50 , 52A07 , 52A10 , 46A50 , 46A55 , 46B50 , 52A07 , 52A10

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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.

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