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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
17. Tychonoff theorem
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Part 1 (pages 118-121)
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Page 118: Tychonoff theorem and centered families of sets.
Page 119: Centered families and compact spaces.
Page 120: Proof of Tychonoff theorem.
Page 121: Products of compact Hausdorff spaces.
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16. Compact metric spaces
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18. Compactification