Topological measures, image transformations and self-similar sets

Summary

This paper introduces a novel idea: the concept of an image transformation. We also introduce the closely related concept of a quasi-homomorphism, and study the properties of these mathematical objects, and give several examples. In particular we investigate iterated systems of image transformations, which we believe give a more realistic approach to the study of so called self-similar structures in nature than what is obtained by iterated function systems.