Book Description:This text suitable for postgraduate students in mathematics offers a clear, comprehensive presentation of the fundamentals of topology. It can also be effectively used at the senior undergraduate level for a basic introduction to the core topics of topology. The book's broad coverage of topics and flexible organization allows instructors to follow their own preferences in the matter of course emphasis.
The second edition is divided into two parts-general topology and algebraic topology.
Features:THIS IS HOW THE BOOK IS ORGANIZED - Includes foundational material on set theory and logic.
- Presents the 'irreducible core' of the subject in the first four chapters of Part I that should be included in any introductory topology course.
- Remaining four chapters of Part I explore additional topics, to be taken in any order.
- Substantially expanded and re-written topic of algebraic topology now constitutes Part II of the book-nearly a semester's worth of teaching.
- Supplementary exercises at the ends of several chapters provide an opportunity for exploration of topics that diverge somewhat from the main thrust of the book.
Contents:Preface. A Note to the Reader. Part I: GENERAL TOPOLOGY-Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and Paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. Part II: ALGEBRAIC TOPOLOGY-The Fundamental Group. Separation Theorems in the Plane. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. Bibliography. Index.
About the Author:Massachusetts Institute of Technology
