CI-posets, domínios e espaços de funções

Abstract

In this work, we study posets (partially ordered sets) that are not necessarily continuous but having intervals as continuous posets with induced order. That class of posets associated with the Scott topology plays an important role when the interest is the characterization of the continuous functions space. The study is focused on three hereditary Scott topologies, namely lower hereditary, upper hereditary and weakly upper hereditary, seeking to characterize the space of continuous functions defined from a core compact space X to a poset P such that is equipped with a hereditary Scott topology and satisfying some additional conditions.