The Function (and the Functor) Ac(t) of the open closed subsets of a Topological space (x,t) were analysed. The analysis was made first when X is fixed, in the context of the adjoint functions, with the corresponding study of fixed points of the adjoint pair (Tx, Acx). x i s variable we rep la ce the study in the context of the adjoi nt contravariant functors and analyse the sense of the adjoinction morphisms.