Syllabus/achievement requirements

The syllabus consists of the lecture notes on projective spaces and matrix groups as well as the following parts of Munkres' textbook:

 

Chapter 1: Set Theory and Logic (regarded as background material)

Chapter 2: Topological Spaces and Continuous Functions

12. Topological Spaces

13. Basis for a Topology (omitting lower limit and K-topologies)

15. The Product Topology on X x Y

16. The Subspace Topology

17. Closed Sets and Limit Points

18. Continuous Functions

19. The Product Topology (omitting box topology)

20. The Metric Topology

21. The Metric Topology (continued)

22. The Quotient Topology

Chapter 3: Connectedness and Compactness

23. Connected Spaces

24. Connected Subspaces of the Real Line

25. Components and Local Connectedness

26. Compact Spaces

27. Compact Subspaces of the Real Line

28. Limit Point Compactness

29. Local Compactness

Chapter 4: Countability and Separation Axioms

30. The Countability Axioms

31. The Separation Axioms

32. Normal Spaces

33. The Urysohn Lemma

34. The Urysohn Metrization Theorem

35. The Tietze Extension Theorem

Chapter 7: Complete Metric Spaces and Function Spaces

43. Complete Metric Spaces

45. Compactness in Metric Spaces

46. Pointwise and Compact Convergence

Chapter 8: Baire Spaces and Dimension Theory

48. Baire Spaces

49. A Nowhere-Differentiable Function

Chapter 9: The Fundamental Group

51. Homotopy of Paths

52. The Fundamental Group

53. Covering Spaces

Published Aug. 19, 2019 3:13 PM - Last modified Nov. 17, 2019 3:26 PM