Abstract and Applied Analysis
Volume 2010 (2010), Article ID 375014, 5 pages
Research Article

On the 𝑆 -Invariance Property for 𝑆 -Flows

Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

Received 3 August 2010; Revised 20 October 2010; Accepted 8 November 2010

Academic Editor: Allan C Peterson

Copyright © 2010 Amin Saif and Adem Kılıçman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define an equivalence relation on a topological space which is acted by topological monoid 𝑆 as a transformation semigroup. Then, we give some results about the 𝑆 -invariant classes for this relation. We also provide a condition for the existence of relative 𝑆 -invariant classes.