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

The notion of a 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 in Tychonov powers Rτ of the real line. We show that the corresponding spaces are absolute retracts if and only if τ≤ω1.