On invariant sets topology

Authors

1 Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.

2 Young Researchers Club, Semnan Branch, Islamic Azad University, Semnan, Iran.

Abstract

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. f := fA  X : f(A)  Ag  P(X) is a topology on X. Among other things,
we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between f
and To f . For instance, we find the conditions on f to show that whenever f is T0, T1 or T2.

Keywords