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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
10. Urysohn lemma
Notes
Complete lecture notes
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Videos
Part 1 (pages 78-79)
Part 2 (page 80)
Part 3 (page 81)
Page links
Page 78: Introduction.
Page 79: Key lemma.
Page 80: Proof of the Urysohn lemma.
Page 81: Completely regular spaces.
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9. Separation axioms
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11. Tietze extension theorem