Author(s): C.T.C. Wall
Publisher: Addison Wesley Publishing Company
Year: 1972
PART 0 PRELIMINARIES
Chapter 0 Notations and Prerequisites
Numbers
Sets and maps
Equivalence relations
Chapter 1 Spaces and Continuous Maps
Introduction
Continuity
Homeomorphism
Neighborhoods, open and closed sets
Compactness
Chapter 2 Abelian Groups
Introduction
Definitions
Direct sums
Exact sequences
Free abelian groups
PART 1 INTRODUCTION TO HOMOTOPY THEORY
Chapter 3 Connected and Disconnected Spaces
Introduction
Connectedness
Path-connectedness
Local path-connectedness
Chapter 4 More about Connection
Introduction
The group H0(X)
The set π0(X)
The group H0(X)
Chapter 5 Definition of Homotopy
Introduction
Definition of homotopy
Homotopy equivalence
Homotopy sets; the groups H1(X)
Chapter 6 A Study of a Circle
Introduction
Lifting maps from S1 up to R
The degree of a map
Applications
Chapter 7 Lifting and Extension Problems
Introduction
The lifting problem
The extension problem
Chapter 8 Calculations
Introduction
The Mayer-Vietoris theorem
First calculations
Graphs
Products
PART 2 THE DUALITY THEOREM
Chapter 9 Eilenberg's Separation Criterion
Introduction
Complementary components
Separation of points by compact plane sets
Chapter 10 The Duality Map
Introduction
Construction of the duality map
Proof of injectivity
Chapter 11 Proof of the Duality Theorem
Introduction
An extension theorem
Naturality
Proof in some special cases
End of the proof
Chapter 12 Remarks on the Proof
Introduction
The extended plane
Reformulation of preceding chapters
The Hopf map
PART 3 FURTHER RESULTS IN THE TOPOLOGY OF PLANE SETS
Chapter 13 The Jordan Curve Theorem
Introduction
Theta curves
First alternative proof (after Dieudonne)
Point sets in Rn and Sn
Second alternative proof (after Doyle)
Invariance of (plane) domains
Chapter 14 Further Duality Properties
Introduction
The group H1(X)
Properties of Hl(X)
Duality
Plane domains
Chapter 15 Geometric Integration Theory
Introduction
Line integrals in R2
Green's theorem
Reformulation in terms of homology
The three-dimensional case
The complex case
Index of Terms
Index of Notation
