• schedule
  • resources
  • Discord
  • Gradescope
Previous module:
schedule

  • 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

18. Compactification

Notes

  • Complete lecture notes
  • Blank lecture notes

Videos

Part 1 (pages 122-124)

Part 2 (pages 125-126)

Part 3 (pages 127-129)

Page links

  • Page 122: Definition of a compactification.
  • Page 123: Some examples.
  • Page 124: Existence of compactifications.
  • Page 125: Ordering of compactifications.
  • Page 126: Maximality of the Cech-Stone compactification.
  • Page 127: One-point compactifications and locally Hausdorff spaces.
  • Page 128: Existence of one-point compactifications.
  • Page 129: Closing remarks.

Previous section:
17. Tychonoff theorem
Next section:
19. Quotient spaces
CC-BY-SA Icon

All the materials on this site are licensed under a Creative Commons BY-NC-SA 4.0 International license.