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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 790758, 14 pages
http://dx.doi.org/10.1155/2012/790758
Research Article

The Structure of Disjoint Groups of Continuous Functions

Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71457-44776, Iran

Received 14 February 2012; Accepted 24 April 2012

Academic Editor: Sung Guen Kim

Copyright © 2012 Hojjat Farzadfard and B. Khani Robati. 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.

Abstract

Let I be an open interval. We describe the general structure of groups of continuous self functions on I which are disjoint, that is, the graphs of any two distinct elements of them do not intersect. Initially the class of all disjoint groups of continuous functions is divided in three subclasses: cyclic groups, groups the limit points of their orbits are Cantor-like sets, and finally those the limit points of their orbits are the whole interval I. We will show that (1) each group of the second type is conjugate, via a specific homeomorphism, to a piecewise linear group of the same type; (2) each group of the third type is a subgroup of a continuous disjoint iteration group. We conclude the Zdun's result on the structure of disjoint iteration groups of continuous functions as special case of our results.