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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

19. Quotient spaces

Notes

  • Complete lecture notes
  • Blank lecture notes

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
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