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
16. Compact metric spaces
Notes
Complete lecture notes
Blank lecture notes
Videos
Part 1 (pages 113-114)
Part 2 (pages 115-117)
Page links
Page 113: Sequentially compact spaces.
Page 114: Compact metric spaces are sequentially compact.
Page 115: Lebesgue number of an open cover.
Page 116: ε-nets.
Page 117: sequentially compact metric spaces are compact.
Previous section:
15. Heine-Borel theorem
Next section:
17. Tychonoff theorem