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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
2. Metric spaces
Notes
Complete lecture notes
Blank lecture notes
Videos
Part 1 (pages 16-20)
Part 2 (pages 21-25)
Page links
Page 16: Continuous functions of a single variable.
Page 17: Continuous functions of many variable.
Page 18: Open balls in real spaces.
Page 19: Metric spaces and continuous functions.
Page 20: Open balls in metric spaces.
Page 21: Euclidean metric.
Page 22: Orthogonal metric.
Page 23: Maximum metric.
Page 24: Hub metric.
Page 25: Discrete metric. Subspace of a metric space.
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3. Open sets