-subgroups of ordered groups
We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.
A zone diagram of order n is a relatively new concept which was first defined and studied by T. Asano, J. Matoušek and T. Tokuyama. It can be interpreted as a state of equilibrium between n mutually hostile kingdoms. Formally, it is a fixed point of a certain mapping. These authors considered the Euclidean plane with finitely many singleton-sites and proved the existence and uniqueness of zone diagrams there. In the present paper we generalize this concept in various ways. We consider general sites...