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. $\tau_f := \{A\subseteq X : f(A)\subseteq A\}\subseteq \mathcal{P}(X)$ is a topology on $X$. Among other things, we find the smallest open sets contains a point $x\in X$. Moreover, we find the relations between $f$ and $\tau_f$ . For instance, we find the conditions on $f$ to show that whenever $\tau_f$ is $T_0, T_1$ or $T_2$.
Eshaghi Gordji,M and 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
MLA
Eshaghi Gordji,M , and Rostamian Delavar,M . "On invariant sets topology", International Journal of Nonlinear Analysis and Applications, 5, 2, 2014, 31-36. doi: 10.22075/ijnaa.2014.124
HARVARD
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
CHICAGO
M Eshaghi Gordji and 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
VANCOUVER
Eshaghi Gordji M, Rostamian Delavar M. On invariant sets topology. IJNAA. 2014;5(2):31-36. doi: 10.22075/ijnaa.2014.124
International Journal of Nonlinear Analysis and Applications