## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2012 (2012), Article ID 790758, 14 pages.

### The Structure of Disjoint Groups of Continuous Functions

Hojjat Farzadfard and B. Khani Robati

#### 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.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2012 (2012), Article ID 790758, 14 pages.

**Dates**

First available in Project Euclid: 14 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1355495743

**Digital Object Identifier**

doi:10.1155/2012/790758

**Mathematical Reviews number (MathSciNet)**

MR2935145

**Zentralblatt MATH identifier**

1284.26006

#### Citation

Farzadfard, Hojjat; Khani Robati, B. The Structure of Disjoint Groups of Continuous Functions. Abstr. Appl. Anal. 2012 (2012), Article ID 790758, 14 pages. doi:10.1155/2012/790758. https://projecteuclid.org/euclid.aaa/1355495743