Principles of Topology

Description

This text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological equivalence, basis, sub-basis, connectedness , compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces are treated in this text. Most of the factual information about topology presented in this text is stated in the theorems and illustrated in the accompanying examples, figures and exercises. This book contains many exercises of varying degrees of difficulty. The notation used in this text is reasonably standard; a list of symbols with definitions appears on the front end-sheets. This text is designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels. It is accessible to junior mathematics majors who have studied multivariable calculus. FeaturesA brief summary of a modest amount of prerequisite material on sets and functions required for the remainder of the course.Topological concepts in the familiar setting of the real line and Euclidean plane.Euclidean spaces and Hilbert space, geometric applications are emphasizedContentsPreface CHAPTER 1. INTRODUCTION CHAPTER 2. THE LINE AND THE PLANE CHAPTER 3. METRIC SPACES CHAPTER 4. TOPOLOGICAL SPACES CHAPTER 5. CONNECTEDNESS CHAPTER 6. COMPACTNESS CHAPTER 7. PRODUCT AND QUOTIENT SPACES CHAPTER 8. SEPARATION PROPERTIES AND METRIZATION CHAPTER 9. THE FUNDAMENTAL GROUP APPENDIX: INTRODUCTION TO GROUPS Bibliography Index