Dimension-raising Homomorphisms between Lattices of Convex Bodies

الأصل · EN

We settle the first unsolved case of a problem of P. M. Gruber, asked by him in 1991, namely, to investigate the homomorphisms from the lattice of convex bodies of Eᶜ to the lattice of convex bodies of Eᵈ for c<d. We completely describe these homomorphisms for the case d=c+1, for c ≥ 3. The obtained result is then applied to characterize anti-homomorphisms and homomorphisms from lattices of convex bodies to lattices of convex functions.