THE T₀-REFLECTION IN THE CATEGORY V-PRETOP

A V-pretopological space is a pair (X, a) where X is a nonempty set and a is a (Formula presented) self map satisfying (Formula presented) and (Formula presented) for any (Formula presented). It is well known that the category Top of topological spaces is a reflective subcategory in the category V-PreTop whose objects are pretopological spaces of type V. In the present paper we give the construction of the T₀-reflection in the category V-PreTop. Hence, some new separation axioms are introduced and characterized. Finally, the orthogonal of some subcategories are studied.