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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
14. Compact spaces
Notes
Complete lecture notes
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Videos
Part 1 (pages 103-105)
Part 2 (pages 106-108)
Part 3 (page 109)
Page links
Page 103: Open covers and compact spaces.
Page 104: Some examples.
Page 105: Closed intervals are compact.
Page 106: Compact spaces and continuous functions.
Page 107: Compact spaces and closed sets.
Page 108: Homeomorphisms of compact Hausdorff spaces.
Page 109: Compact Hausdorff spaces are normal.
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13. Metrization of manifolds
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15. Heine-Borel theorem