Weakness of the topological twin building of a masure for the cone topology

Masures are generalizations of Bruhat-Tits buildings introduced by Gaussent and Rousseau in order to study Kac-Moody groups over valued fields. A masure admits a building at infinity Ch(∂∆), which is a twin building. Ciobotaru, Mühlherr and Rousseau equipped Ch(∂∆) with a topology called the cone topology. They proved that this equips Ch(∂∆) with a structure of weak topological twin building in the definition of Hartnick, Köhl and Mars. In this note, we prove however that unless G is reductive, Ch(∂∆) is not a topological twin building