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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
15. Heine-Borel theorem
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Part 1 (pages 110-112)
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Page 110: Bounded sets and Heine-Borel theorem.
Page 111: Products of compact spaces.
Page 112: Proof of Heine-Borel theorem.
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14. Compact spaces
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16. Compact metric spaces