T₀-SEPARATION IN TOPOLOGICAL CATEGORIES

R.-E. Hoffmann [5,6] has introduced the notion of an (E,M)-universally topological functor, which provides a categorical characterization of the T0-separation axiom of general topology. In this paper, we characterise these functors in terms of the unique extension of structure functors defined on the subcategory of “separated” objects (of the domain category). This, in turn, leads to a solution of some problems due to G.C.L. Brümmer [1,2]. Other results include a generalization of L. Skula's characterization of the bireflective subcategories of Top [10].