This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.
Ch 1 Set Theory and Logic
Ch 2 Topological Spaces and Continuous Functions
Ch 3 Connectedness and Compactness
Ch 4 Countability and Separation Axioms
Ch 5 The Tychonoff Theorem
Ch 6 Metrization Theoremss and Paracompactness
Ch 7 Complete Metric Spaces and Function Spaces
Ch 8 Baire Spaces and Dimension Theory
Ch 9 The Fundamental Group
Ch10 Separation Theorems in the Plane
Ch11 The Seifert-van Kampen Theorem
Ch12 Classification of Surfaces
Ch13 Classification of Covering Spaces