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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
19. Quotient spaces
Notes
Complete lecture notes
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Videos
Part 1 (pages 130-132)
Part 2 (pages 133-135)
Part 3 (page 136)
Page links
Page 130: Equivalence relations.
Page 131: Equivalence classes and the quotient map.
Page 132: Quotient topology.
Page 133: Examples: cylinder the Möbius band.
Page 134: Examples: torus and the Klein bottle.
Page 135: Examples: 2-dimensional real projective space
Page 136: Disjoint union of spaces.
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18. Compactification