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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

7. Connectedness

Notes

  • Complete lecture notes
  • Blank lecture notes

Videos

Part 1 (page 60)

Part 2 (page 61)

Part 3 (pages 62-63)

Part 4 (page 64)

Page links

  • Page 60: Motivation. Definition of connected space.
  • Page 61: Connectedness of intervals.
  • Page 62: Connectedness and homeomorphisms. Intermediate value theorem. Topological invariants.
  • Page 63: Further properties of connected spaces.
  • Page 64: Connected components.

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6. Continuous functions
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8. Path connectedness
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