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  • User guide
  • 1. Some set theory
  • 2. Metric spaces
  • 3. Open sets
  • 4. Basis, subbasis, subspace
  • 5. Closed sets
  • 6. Continuous functions
  • 7. Connectedness
  • 8. Path connectedness
  • 9. Separation axioms
  • 10. Urysohn lemma
  • 11. Tietze extension theorem
  • 12. Urysohn metrization theorem
  • 13. Metrization of manifolds
  • 14. Compact spaces
  • 15. Heine-Borel theorem
  • 16. Compact metric spaces
  • 17. Tychonoff theorem
  • 18. Compactification
  • 19. Quotient spaces

2. Metric spaces

Notes

  • Complete lecture notes
  • Blank lecture notes

Videos

Part 1 (pages 16-20)

Part 2 (pages 21-25)

Page links

  • Page 16: Continuous functions of a single variable.
  • Page 17: Continuous functions of many variable.
  • Page 18: Open balls in real spaces.
  • Page 19: Metric spaces and continuous functions.
  • Page 20: Open balls in metric spaces.
  • Page 21: Euclidean metric.
  • Page 22: Orthogonal metric.
  • Page 23: Maximum metric.
  • Page 24: Hub metric.
  • Page 25: Discrete metric. Subspace of a metric space.

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1. Some set theory
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3. Open sets
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