Introduction

Summary

To a large extent this book is an updated version of Lectures on Topological Dynamics by Robert Ellis [Ellis, R., (1969)]. That book gave an exposition of what might be called an algebraic theory of minimal sets. Our goal here is to give a clear, self contained exposition of a new approach to the theory which allows for more straightforward proofs and develops a clearer language for expressing many of the fundamental ideas. We have included a treatment of many of the results in the aforementioned exposition, in addition to more recent developments in the theory; we have not attempted, however, to give a complete or exhaustive treatment of all the known results in the algebraic theory of minimal sets. Our hope is that the reader will be motivated to use the language and techniques to study related topics not touched on here. Some of these are mentioned either in the exercises or notes given at the end of various sections. This book should be suitable for a graduate course in topological dynamics whose prerequisites need only include some background in topology. We assume the reader is familiar with compact Hausdorff spaces, convergence of nets, etc., and perhaps has had some exposure to uniform structures and pseudo metrics which play a limited role in our exposition.