# Topology and Homotopy

### Illustrations and Tidbits

1. Work in progress. Incomplete plus this clearly needs cleaning...

2. I will use this page for noting 'typos' and typos in the book. These can be found in the pdf behind thefollowing link: ERRATA! So far we have found 27 typos and 'typos'.

(There is a solution manual associated with this book, part 1 (published by CRC, 2017). Here is the Errata-Solution-Manual file!)

PART 1: TOPOLOGY

 Chapter 1: Sets and Numbers Section 1.1 Sets Section 1.2 Cardinal Numbers Section 1.3 Axiom of Choice
 Chapter 2: Metric Spaces Section 2.1 Metric Spaces: definition and examples (contains extras) Section 2.2 Metric Spaces: basics
 Chapter 3: Topological Spaces Section 3.1 Topological Spaces: definition and basic examples (contains extras) Section 3.2 Topological Spaces: basic notions Section 3.3 Bases Section 3.4 Dense and nowhere dense Section 3.5 Continuous maps
 Chapter 4: Subspaces, Quotients Spaces and Manifolds Section 4.1 Subspaces Section 4.2 Quotient spaces Section 4.3 Sums of spaces and identifying spaces Section 4.4 Manifolds and CW-complexes
 Chapter 5: Products of Spaces Section 5.1 Finite products of spaces Section 5.2 Infinite products of spaces Section 5.3 Box topology
 Chapter 6: Connected and Path Connected Spaces Section 6.1 Connected spaces Section 6.2 Connected spaces: properties Section 6.3 Path connected spaces Section 6.4 Path connected spaces: properties Section 6.5 Locally connected and locally path connected
 Chapter 7: Compactness Section 7.1 Compact spaces Section 7.2 Compact spaces: properties Section 7.3 Compact, Lindelöf, countably compact Section 7.4 Bolzano, Weierstrass, Lebesgue Section 7.5 One-point compactification Section 7.6 Tychonoff theorem
 Chapter 8: Separation Properties Section 8.1 The hierarchy of separation properties Section 8.2 Regular and normal spaces Section 8.3 Normal spaces and subspaces
 Chapter 9:Urysohn, Tietze and Stone-Czech Section 9.1 Urysohn lemma Section 9.2 Tietze extension theorem Section 9.3 Stone-Czech compactification

PART 2: HOMOTOPY

 Chapter 10: Isotopy, Homotopy, Fundamental Group Section 10.1 Isotopy Section 10.2 Homotopy Section 10.3 Homotopy and paths Section 10.4 The fundamental group
 Chapter 11: The Fundamental Group of a Circle Section 11.1 The fundamental group of a circle Section 11.2 Brouwer fixed point and the fundamental theorem of algebra Section 11.3 The Jordan curve theorem
 Chapter 12: Combinatorial Group Theory Section 12.1 Group Presentations Section 12.2 Free groups, Tietze, Dehn (no graphics) Section 12.3 Free products and free products with amalgamation (no graphics)
 Chapter 13: Seifert-Van Kampen Theorem Section 13.1 Seifert - van Kampen theorem Section 13.2 Seifert - van Kampen; examples Section 13.3 Seifert - van Kampen and knots Section 13.4 Torus knots and Alexander horned sphere Section 13.5
 Chapter 14: Classifying Manifolds Section 14.1 Section 14.2 Section 14.3 Section 14.4 Section 14.5
 Chapter 15: Covering Spaces, Part 1 Section 15.1 Section 15.2 Section 15.3 Section 15.4
 Chapter 16: Covering Spaces, Part 2 Section 16.1 Section 16.2 Section 16.3 Section 16.4 Section 16.5
 Chapter 17: Applications in Group Theory Section 17.1 Section 17.2 Section 17.3 Section 17.4