... of {1, 2, . . . , n}.1) When n = 3 the proposition is obvious: if x = (12) we choose y = (123); if x = (123) we choosey = (12).2) n = 4. Let x = (12)(34). Assume that there exists y ∈ Sn, ... ⊆ U1and T(U2) ⊆ U2). Calculate the dimension of Eas a real vector space.Solution First choose a basis {v1, v2, v3} of U1. It is possible to extend this basis with vectors v4,v5andv6to ... points that belong to at least two different spheres from S is countable.Solution. For every x ∈ M choose spheres S, T ∈ S such that S = T and x ∈ S ∩ T ; denote by U, V, Wthe three components...