General

This is the webpage for the course Toplogy (V63.0375) in fall 2010, taught by Sonal Jain (email: lastname at cims dot nyu dot edu).

The regular meeting time is on Tuesdays and Thursdays from 2-3:15pm in Warren Weaver Hall 317. Office hours will be Tuesdays from 3:30-5pm in WWH 619.

Prerequisites: Analysis I or equivalent.

Your grade will be based on ten homework assigments (40%), a midterm exam (20%), and a take home final exam (40%).

Syllabus and references

Set theory, topological spaces, connectedness, compactness, countability and separation axioms, the fundamental goup, covering spaces, applications.

The official text is Topology by Munkres.

Lectures

  1. (9/7) Naive set theory
  2. (9/9) Axiom of choice, well ordered sets
  3. (9/14) Topological spaces, bases;
  4. (9/16) Order, product, subspace topologies;
  5. (9/21) Closed sets, limit points, Hausdorff axiom
  6. (9/23) Continuous functions, homeomorphisms
  7. (9/26) Product topology, Box topology
  8. (9/28) Metric Spaces
  9. (10/5) Metric topology, boundedness, uniform topology
  10. (10/7) Uniform convergence
  11. (10/12) Connected spaces
  12. (10/14) Connected subsets of the real line
  13. (10/19) Compactness
  14. (10/21) Compactness cont.
  15. (10/26) Midterm Exam
  16. (10/28) Recap
  17. (11/2) Compact subsets of the real line
  18. (11/4) Limit point compactness, sequential compactness
  19. (11/9) Local compactness
  20. (11/11) Countability axioms
  21. (11/16) Separation axioms
  22. (11/18) Normal spaces, Urysohn lemma
  23. (11/23) Urysohn metrization theorem
  24. (11/30) Quotient topology
  25. (12/2) Topological groups
  26. (12/7) Homotopy of paths, fundamental group
  27. (12/9) Covering spaces
  28. (12/14) Fundamental theorem of algebra, Borsuk-Ulam theorem.

Assignments

All dates posted below are DUE dates.
  1. (9/14) Problem Set 1
  2. (9/23) Problem Set 2 ;
  3. (9/30) Problem Set 3
  4. (10/7) Problem Set 4
  5. (10/19) Problem Set 5
  6. (11/9) Problem Set 6
  7. (11/16) Problem Set 7
  8. (12/2) Problem Set 8
  9. (12/17) Final