The T0-reflection in the category V-PreTop

Abstract

AV-pretopological space is a pair(X, a)whereXis a nonempty set andais aP(X)self map satisfyinga(∅) =∅,A⊆a(A)anda(A∪B) =a(A)∪a(B)foranyA, B∈ P(X). It is well known that the categoryTopof topological spaces isa reflective subcategory in the categoryV-PreTopwhose objects are pretopologicalspaces of typeV. In the present paper we give the construction of theT0-reflectionin the categoryV-PreTop. Hence, some new separation axioms are introducedand characterized. Finally, the orthogonal of some subcategories are studied.