GENERALIZED WEDGES AND ORDERED SPACES WITH THE RIESZ DECOMPOSITION PROPERTY

Abstract

We study order structures given by generalized directed wedges, which seems to be the right objects in order to suggest the correct generalization of certain definitions and results concerning ordered spaces. So, we use the set of all increasing (resp. decreasing), non-empty, downward (resp. upward)-directed, lower (resp. upper) bounded subsets of a directed wedge possessing the Riesz interpolation property in order to prove a Kantorovic type theorem for mappings between directed ordered spaces satisfying the Riesz interpolation property.