Metric and Topological Spaces
John O'Connor
CONTENTS
Introduction
Some historical background
Some topological ideas
Revision of real analysis
Definition and examples of metric spaces
Convergence in metric spaces
Continuity in metric spaces
Neighbourhoods and open sets in metric spaces
Limit points and closed sets in metric spaces
Topological Motivation
Definition and examples of topologies
Properties of topological spaces
Continuity for topological spaces
The subspace topology
The product topology
The identification topology
More identification spaces
Separation axioms
Connectedness
Pathwise connectedness
Compactness
Sequential compactness
Exercises
Exercises 1
Exercises 2
Exercises 3
Exercises 4
Exercises 5
Exercises 6
Exercises 7
Exercises 8
Exercises 9
JOC MT3822 February 2004