schedule
resources
Discord
Gradescope
Previous module:
schedule
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.
Previous section:
8. Path connectedness
Next section:
10. Urysohn lemma