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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
13. Metrization of manifolds
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Part 1 (pages 97-99)
Part 2 (pages 100-101)
Part 3 (page 102)
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Page 97: Definition of a topological manifold.
Page 98: Examples of a manifolds.
Page 99: Invariance of dimension.
Page 100: Manifolds with boundary.
Page 101: Examples of manifolds with boundary.
Page 102: Metrization theorem for manifolds.
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12. Urysohn metrization theorem
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14. Compact spaces