An Illustrated Introduction to

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 1.2 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 3.4 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
 
 
 
 

 

 

 

 

 

 

 
 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

(The linked material for fair use only; © Sasho Kalajdzievski)

 

 

 

 

 

 

 

 

 

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