Essential Topology

Description

This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra. Springer Undergraduate Mathematics Series......Page 1 Essential Topology......Page 3 Preface......Page 5 Contents......Page 7 1 Introduction......Page 10 2 Continuous Functions......Page 12 3 Topological Spaces......Page 24 Interlude......Page 44 4 Topological Properties......Page 46 5 Deconstructionist Topology......Page 63 Interlude......Page 97 6 Homotopy......Page 98 7 The Euler Number......Page 124 8 Homotopy Groups......Page 134 9 Simplicial Homology......Page 156 10 Singular Homology......Page 174 11 More Deconstructionism......Page 204 Solutions to Selected Exercises......Page 220 Bibliography......Page 224 Index......Page 225