Lower topological algebraic domain models of topological spaces

Abstract

The maximal point space of a domain (resp. algebraic domain) with the Scott topology is Choquet complete. Thus, not every T₁ topological space can be represented as the maximal point space of some algebraic domain equipped with the Scott topology. However, in this paper, we prove that: (1) Every T₁ topological space is homeomorphic to the set of all maximal points of some algebraic domain equipped with the relative lower topology. (2) Bounded complete domains endowed with the lower topology are Choquet complete.