Topology Course Notes Harvard University Math 131. Fall 2013. C. McMullen Contents 1 Introduction .. 1. 2 Background in set theory .. 3. 3 Topology .. 12. 4 Connected spaces .. 23. 5 Compact spaces .. 27. 6 Metric spaces .. 32. 7 Normal spaces .. 41. 8 Algebraic Topology and homotopy theory .. 45. 9 Categories and paths .. 47. 10 Path lifting and covering spaces .. 53. 11 Global Topology : applications .. 58. 12 Quotients, gluing and simplicial complexes .. 61. 13 Galois theory of covering spaces .. 66. 14 Free groups and graphs .. 75. 15 Group presentations, amalgamation and gluing .. 81. 1 Introduction Topology is simply geometry rendered flexible. In geometry and analysis, we have the notion of a metric space, with distances specified between points. But if we wish, for example, to classify surfaces or knots, we want to think of the objects as rubbery.
This course. This course correspondingly has two parts. Part I is point{set topology, which is concerned with the more analytical and aspects of the
Tags:
Analytical, Topology