Math 636 (Topology I)

Class hours

  MWF      11:30 - 12:20                 ZACH 105D

Homeworks:

Problem set 1 (due 9/13)
Problem set 2 (due 9/20)
Training homework
Problem set 3 (due 10/13)
Problem set 4 (due 10/20)
Training homework 2
Problem set 5 (due 11/10)
Problem set 6 (due 11/20)
Problem set 7 (due 11/27)
Training homework 3

Course Syllabus

• PDF file
• HTML
  

Help outside of classes

• Office hours: Tuesday and Thursday 9:40-11:00 AM or by appointment.

Lectures

1. Aug 28 Introduction. Set theory review. (Appendix B)
   
2. Aug 30
   
3. Sep 1
   
4. Sep 4 Metric spaces and their topology.
   
5. Sep 6 Topological spaces.
   
6. Sep 8 Basis of a topology.
   
7. Sep 11 Examples of topological spaces.
8. Sep 13 Subspaces. Interior and closure. 
   
9. Sep 15 Connected components.
10. Sep 18 Connected components.                                 material for Exam 1                                
    
11. Sep 20 Separation axioms
    
12. Sep 22 Convergence
    
13. Sep 25 Review
    
14. Sep 27 Exam 1
    
15. Sep 29 Nets and convergence
    
16. Oct 2 Compactness
17. Oct 4 Compactness
    
18. Oct 6 Products
    
19. Oct 9 Products and Tykhonov theorem
    
20. Oct 11 Products and Tykhonov theorem
    
21. Oct 13 Cantor set and plane-filling curves
    
22. Oct 16 Compact metric spaces
    
23. Oct 18 Compact metric spaces                                    material for Exam 2                               
    
24. Oct 20 Products of metric spaces
    
25. Oct 23 A metrization theorem
    
26. Oct 25  Review
    
27. Oct 27  Exam 2
    
28. Oct 30
29. Nov 1
30. Nov 3
31. Nov 6
32. Nov 8
33. Nov 10
34. Nov 13
35. Nov 15
36. Nov 17
37. Nov 20
38. Nov 22
39. Nov 27
40. Nov 29
41. Dec 1  Review
    
42. Dec 4  Review
    

Dec 13 Final Exam