1 Introduction
1.1 Explanatory Notes
1.2 n-Space
1.3 Abstraction
2 Topological Space
2.1 Topological space
2.2 Semimetric and metric space
2.3 Semimetric and metric topologies
2.4 Natural topologies and metrics
2.5 Notation and terminology
2.6 Base and subbase
3 Convergence
3.1 Sequences
3.2 Filters
3.3 Partially ordered sets
3.4 Nets
3.5 Arithmetic of nets
4 Separation Axioms
4.1 Separation by open sets
4.2 Continuity
4.3 Separation by continuous functions
5 Topological Concepts
5.1 Topological properties
5.2 Connectedness
5.3 Separability
5.4 Compactness
6 Sup, Weak, Product and Quotient Topologies
6.1 Introduction
6.2 Sup topologies
6.3 Weak topologies
6.4 Products
6.5 Quotients
6.6 Continuity
6.7 Separation
7 Compactness
7.1 Countable and sequential compactness
7.2 Compactness in semimetric space
7.3 Ultrafilters
7.4 Products
8 Compactification
8.1 The one-point compactification
8.2 Embeddings
8.3 The Stone-Cech compactification
8.4 Compactifications
8.5 C- and C*-embedding
8.6 Realcompact spaces
9 Complete Semimetric Space
9.1 Completeness
9.2 Completion
9.3 Baire category
10 Metrization
10.1 Separable spaces
10.2 Local finiteness
10.3 Metrization
11 Uniformity
11.1 Uniform space
Il.2 Uniform continuity
11.3 Uniform concepts
11.4 Uniformization
11.5 Metrization and completion
12 Topological Groups
12.1 Group topologies
12.2 Group concepts
12.3 Quotients
12.4 Topological vector spaces
13 Function Spaces
13.1 The compact open topology
13.2 Topologies of uniform convergence
13.3 Equicontinuity
13.4 Weak compactness
14 Miscellaneous Topics
14.1 Extremally disconnected spaces
14.2 The Gleason map
14.3 Categorical algebra
14.4 Paracompact spaces
14.5 Ordinal spaces
14.6 The Tychonoff plank
14.7 Completely regular and normal spaces
Appendix: Tables of Theorems and Counterexamples
Bibliography
Index