On Invariant Sets Topology

In this paper we introduce and study a new topology related to a self mapping on a nonempty set. Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets of X related to f, i.e. τf := {A ⫃ X : f(A) ⫃ A} ⫃ P(X) is a topology on X. Among other things, we nd the smallest open sets contains a point x 2 X. Moreover, we nd the relations between f and τf . For instance, we nd the conditions on f to show that whenever τf is T0, T1 or T2.