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1 Topological Spaces
1.1 Continuity and Topological Spaces
1.2 Topological Spaces
1.3 Metric Spaces
1.4 Further Examples of Topological Spaces
1.5 Closed Sets
1.6 Hausdor Spaces
1.7 Subspace Topologies
1.8 Continuous Functions between Topological Spaces
1.9 A Criterion for Continuity
1.10 Homeomorphisms
1.11 Product Topologies
1.12 Identi cation Maps and Quotient Topologies
1.13 Compact Topological Spaces
1.14 The Lebesgue Lemma and Uniform Continuity
1.15 Connected Topological Spaces
2 Homotopies and the Fundamental Group
2.1 Homotopies
2.2 The Fundamental Group of a Topological Space
2.3 Simply-Connected Topological Spaces
3 Covering Maps and the Monodromy Theorem
3.1 Covering Maps 28
3.2 Path Lifting and the Monodromy Theorem
3.3 The Fundamental Group of the Circle