Hyperspaces of max-plus convex subsets of powers of the real line

Abstract

The notion of max-plus convex subset of Euclidean space can be naturally extended to other linear spaces. The aim of this paper is to describe the topology of hyperspaces of max-plus convex subsets of Tychonov powers ${\mathbb{R}}^{\tau }$ of the real line. We show that the corresponding spaces are AR's if and only if $\tau \le {\omega }_1$.