Metric and Topological Spaces

John O'Connor

CONTENTS

  1. Introduction
  2. Some historical background
  3. Some topological ideas
  4. Revision of real analysis
  5. Definition and examples of metric spaces
  6. Convergence in metric spaces
  7. Continuity in metric spaces
  8. Neighbourhoods and open sets in metric spaces
  9. Limit points and closed sets in metric spaces
  10. Topological Motivation
  11. Definition and examples of topologies
  12. Properties of topological spaces
  13. Continuity for topological spaces
  14. The subspace topology
  15. The product topology
  16. The identification topology
  17. More identification spaces
  18. Separation axioms
  19. Connectedness
  20. Pathwise connectedness
  21. Compactness
  22. Sequential compactness
Exercises
  1. Exercises 1
  2. Exercises 2
  3. Exercises 3
  4. Exercises 4
  5. Exercises 5
  6. Exercises 6
  7. Exercises 7
  8. Exercises 8
  9. Exercises 9
JOC MT3822 February 2004