On invariant sets topology

Authors

  • M. Eshaghi Gordji Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.
  • M. Rostamian Delavar 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 ofX 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 fand To f . For instance, we find the conditions on f to show that whenever f is T0, T1 or T2.

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Journal title

volume 5  issue 2

pages  31- 36

publication date 2014-07-01

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