Title of article
On Invariant Sets Topology
Author/Authors
Eshaghi Gordji, Madjid Department of Mathematics - Semnan University, Semnan , Rostamian Delavar, Mohsen Islamic Azad University, Semnan
Pages
6
From page
31
To page
36
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. τf := {A ⫃ X : f(A) ⫃ A} ⫃ P(X) is a topology on X. Among other things,
we nd the smallest open sets contains a point x 2 X. Moreover, we nd the relations between f
and τf . For instance, we nd the conditions on f to show that whenever τf is T0, T1 or T2.
Keywords
Topological spaces , Separation axioms , Fixed point theorems
Journal title
Astroparticle Physics
Serial Year
2014
Record number
2441798
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