Uniqueness of the Inversive Plane of Order 5.
Given a quadratic extension L/K of fields and a regular λ-Hermitian space (V, h) of finite dimension over L, we study the orbits of the group of isometries of (V, h) in the set of hyperbolic K-substructures of V.
The aim of the paper is to prove that the bounded and unbounded Urysohn universal spaces have unique (up to isometric isomorphism) structures of metric groups of exponent 2. An algebraic-geometric characterization of Boolean Urysohn spaces (i.e. metric groups of exponent 2 which are metrically Urysohn spaces) is given.