Internal Neighbourhood Structures II: Closure and closed morphisms

Internal preneighbourhood spaces were first conceived inside any finitely complete category with finite coproducts and proper factorisation structure in my earlier paper. In this paper a closure operation is introduced on internal preneighbourhood spaces and investigated along with closed morphisms and its close allies. Analogues of several well known classes of topological spaces for preneighbourhood spaces are investigated. The approach via preneighbourhood systems is shown to be more general than the closure operators and conveniently allows to identify properties of classes of morphisms which are independent of continuity of morphisms with respect to closure operators.