The rational Gurarii space and its linear isometry group
Volume 289 / 2026
Studia Mathematica 289 (2026), 79-99
MSC: Primary 54H11; Secondary 46B20, 03E15
DOI: 10.4064/sm250501-5-12
Published online: 8 June 2026
Abstract
We show that the classes of partial isometries in finite-dimensional polyhedral spaces and in finite-dimensional rational polyhedral spaces do not have the weak amalgamation property. This implies that the linear isometry group of the rational Gurarii space does not have a comeager conjugacy class. Our methods also demonstrate that the classes of finite-dimensional polyhedral spaces and of finite-dimensional rational polyhedral spaces fail to have the Hrushovski property.
