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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

16. Compact metric spaces

Notes

  • Complete lecture notes
  • Blank lecture notes

Videos

Part 1 (pages 113-114)

Part 2 (pages 115-117)

Page links

  • Page 113: Sequentially compact spaces.
  • Page 114: Compact metric spaces are sequentially compact.
  • Page 115: Lebesgue number of an open cover.
  • Page 116: ε-nets.
  • Page 117: sequentially compact metric spaces are compact.

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15. Heine-Borel theorem
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17. Tychonoff theorem
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