Abstract
In this paper the lattice of all epireflective subcategories of a topological category is studied by defining the T 0-objects of a topological category. A topological category is called universal iff it is the bireflective hull of its T 0-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.
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