Eshaghi Gordji, M., Rostamian Delavar, M. (2014). On invariant sets topology. International Journal of Nonlinear Analysis and Applications, 5(2), 31-36. doi: 10.22075/ijnaa.2014.124
M. Eshaghi Gordji; M. Rostamian Delavar. "On invariant sets topology". International Journal of Nonlinear Analysis and Applications, 5, 2, 2014, 31-36. doi: 10.22075/ijnaa.2014.124
Eshaghi Gordji, M., Rostamian Delavar, M. (2014). 'On invariant sets topology', International Journal of Nonlinear Analysis and Applications, 5(2), pp. 31-36. doi: 10.22075/ijnaa.2014.124
Eshaghi Gordji, M., Rostamian Delavar, M. On invariant sets topology. International Journal of Nonlinear Analysis and Applications, 2014; 5(2): 31-36. doi: 10.22075/ijnaa.2014.124
1Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.
2Young 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.
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