On epireflective subcategories of topological categories

Abstract

In this paper the lattice of all epireflective subcategories of a topological category is studied by defining the T₀-objects of a topological category. A topological category is called universal iff it is the bireflective hull of its T₀-objects. Topological spaces, uniform spaces, and nearness spaces form universal categories. The lattice of all epireflective subcategories of a universal topological category splits into two isomorphic sublattices. Some relations and consequences of this fact with respect to cartesian closedness and simplicity of epireflective subcategories are obtained.