Hyperspaces of max-plus convex subsets of powers of the real line
  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 $\tau\le\omega_1$. 
Lidia Bazylevych, Du\v{s}an Repov\v{s} and Mykhailo Zarichnyi
math.GN math.FA math.GT