I view this book as an introduction to Topology with major emphasis on applications;
it will adequately prepare students for further work in many mathematical disciplines.
The material is organized so that one gets to significant applications quickly, with
emphasis on the geometric understanding and use of new concepts. The theme of this
book is that Topology really is the universal language of modern mathematics.
We assume that the reader has a good grasp of the fundamentals of Logic and Set
Theory, even though a rather succinct review appears in the introductory chapter 0.
The reader should also be very familiar with elementary analysis. Some familiarity
with Group Theory is required for chapters 5, 6 and 8.
The problems which appear at the end of each chapter not only provide ample
opportunity for applying the concepts and techniques just learned but also are used to
introduce additional concepts and techniques which complement the text and point to
further study elsewhere.
I am indebted to many students who, over many years, have made very useful
suggestions on the presentation that follows. I am also indebted to Ida Orahood, Lori
Carranza and Josh Walters who typed the first drafts of this book, and I am especially
indebted to John Gehrmann who did the final revision of the text. I am also very
indebted to Dr. Sunil Nair who encouraged me and helped me publish this book