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  • 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

11. Tietze extension theorem

Notes

  • Complete lecture notes
  • Blank lecture notes

Videos

Part 1 (page 82)

Part 2 (page 83)

Part 3 (page 84)

Part 4 (page 85)

Part 5 (page 86)

Part 6 (page 87)

Page links

  • Page 82: Introduction.
  • Page 83: Sequences of functions.
  • Page 84: Limits of uniformly convergent sequences.
  • Page 85: Approximated extension of a function.
  • Page 86: Proof of the Tietze extension theorem.
  • Page 87: Tietze extension theorem for unbounded functions.

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10. Urysohn lemma
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12. Urysohn metrization theorem
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