Chapter 1 Introduction Exercises 1 Selected Solutions 1 Chapter 2 Topological Spaces 2.1.Topological structures 2.2.Subspace topology 2.3.Covers 2.4.Point position with respect to a set 2.5.Metrics and the metric topology Exercises 2 Selected Solutions 2 Chapter 3 Continuous Maps and Homeomorphisms 3.1.Continuous maps 3.2.Homeomorphisms 3.3.Topological properties Exercises 3 Selected Solutions 3 Chapter 4 Connectedness 4.1.Connected spaces 4.2.Path-Connectedness Exercises 4 Selected Solutions 4 Chapter 5 Separation and Countability Axioms 5.1.Axioms To, T1, T2, T3, and T4 5.2.Hausdorff spaces 5.3.Regular spaces and normal spaces 5.4.Countability axioms Exercises 5 Selected Solutions 5 Chapter 6 Compactness 6.1.Compact spaces 6.2.Interaction of compactness with other topological properties 6.3.Gromov-Hausdorff distance Exercises 6 Selected Solutions 6 Chapter 7 Product Spaces and Quotient Spaces 7.1.Product spaces 7.2.Quotient spaces Exercises 7 Selected Solutions 7 Appendix A Some Elementary Inequalities Bibliography Author Index Subject Index