@article {
author = {Eshaghi Gordji, M. and Rostamian Delavar, M.},
title = {On invariant sets topology},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {5},
number = {2},
pages = {31-36},
year = {2014},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2014.124},
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. $\tau_f := \{A\subseteq X : f(A)\subseteqÂ A\}\subseteq \mathcal{P}(X)$ 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 $T_2$.},
keywords = {Topological spaces,Separation axioms,fixed point theorems},
url = {https://ijnaa.semnan.ac.ir/article_124.html},
eprint = {https://ijnaa.semnan.ac.ir/article_124_5a349c59eb163ba27e34e1903588d147.pdf}
}