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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

9. Separation axioms

Notes

  • Complete lecture notes
  • Blank lecture notes

Videos

Part 1 (pages 71-73)

Part 2 (pages 74-77)

Page links

  • Page 71: $T_1$ spaces.
  • Page 72: $T_2$ (Hausdorff) spaces.
  • Page 73: $T_3$ (regular) spaces and $T_4$ (normal) spaces.
  • Page 74: Metric spaces are normal: preparation.
  • Page 75: Continuity of the distance function.
  • Page 76: Metric spaces are normal: proof.
  • Page 77: Summary of separation axioms.

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8. Path connectedness
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10. Urysohn lemma
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