(f + g,h) = (f,h∗) + (g,h) and (αf,g) = α(f,g); 3. The identity map for the euclidean norm (i.e. 15-11 Completing the Euclidean Plane. Havin a … That is, we construct the real projective plane Π = … If these laws hold, the space is called Euclidean. Continuous preferences in Euclidean space Assume that the choice set X is a subset of Euclidean n-space