A Geometric Introduction to Topology

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