A First Course in Algebraic Topology [Paperback]

This self-contained introduction to algebraic topology is suitable for a number of topology courses.This self-contained introduction to algebraic topology is suitable for a number of topology courses. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout.This self-contained introduction to algebraic topology is suitable for a number of topology courses. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout.This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.Preface; Sets and groups; 1. Background: metric spaces; 2. Topological spaces; 3. Continuous functions; 4. Induced topology; 5. Quotient topology (and groups acting on spaces); 6. Product spaces; 7. Compact spaces; 8. Hausdorff spaces; 9. Connected spaces; 10. The pancake problems; 11. Manifolds and surfaces; 12. Paths and path connected spaces; 12A. The Jordan curve theorem; 13. Homotopy of continuous mappings; 14. 'Multiplication' of paths; 15. The fundamental group; 16. The lr