Point-Set Topology: A Working Textbook

Preface
Contents
1 Introduction
2 Topological Spaces
2.1 Topological Spaces and Examples
2.2 Basis for a Topology
2.3 The Euclidean Topology
2.4 Subbasis for a Topology
2.5 Topological Subspaces
2.6 Worked Exercises
2.7 Suggested Exercises
3 Proximity on a Topological Space
3.1 Neighborhoods of a Point
3.2 Basis of Neighborhoods
3.3 Interior and Closure
3.4 Convergence of Sequences
3.5 Worked Exercises
3.6 Suggested Exercises
4 Metric Spaces
4.1 Distance and Metric Spaces
4.2 Topology on a Metric Space
4.3 Interior and Closure in a Metric Space
4.4 Convergence of Sequences in a Metric Space
4.5 Worked Exercises
4.6 Suggested Exercises
5 Continuity
5.1 Continuous Mappings
5.2 Properties of Continuous Maps
5.3 Continuous Maps on Euclidean Spaces
5.4 Worked Exercises
5.5 Suggested Exercises
6 Homeomorphisms and Topological Invariants
6.1 Homeomorphisms
6.2 Topological Invariants
6.3 Construction of Homeomorphisms in Euclidean Spaces
6.4 Embeddings and Open Maps
6.5 Worked Exercises
6.6 Suggested Exercises
7 Product Topology
7.1 The Product Topology
7.2 Product Topology and Continuity
7.3 Product Topology: The Infinite Case
7.4 Worked Exercises
7.5 Suggested Exercises
8 Connectedness
8.1 Connected Spaces and Examples
8.2 Further Properties of Connectedness
8.3 Connected Components
8.4 Path Connectedness
8.5 Worked Exercises
8.6 Suggested Exercises
9 Compactness
9.1 Compact Spaces and Examples
9.2 Compactness in Euclidean Spaces
9.3 Worked Exercises
9.4 Suggested Exercises
10 Quotient Topology
10.1 Motivation and Definition of the Quotient Topology
10.2 Final Topology and Identifications
10.3 Construction of Homeomorphisms in a Quotient Space
10.4 Maps Between Quotient Spaces
10.5 Worked Exercises
10.6 Suggested Exercises
11 The Fundamental Group
11.1 Homotopy and Loops
11.2 The Fundamental Group of S1
11.3 The Fundamental Group of Sn, n≥2
11.4 Retractions
11.5 Worked Exercises
11.6 Suggested Exercises
Bibliography
Index