Exam Syllabus

The syllabus (pensum) for the examination consists of the following sections of Munkres' textbook:

Chapter 1: Set Theory and Logic

1. Fundamental Concepts

2. Functions

3. Relations

5. Cartesian Products

6. Finite Sets

7. Countable and Uncountable Sets

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 (omitting proof)

36. * Imbeddings of Manifolds

Chapter 5: The Tychonoff Theorem

37. The Tychonoff Theorem (omitting proof)

Chapter 7: Complete Metric Spaces and Function Spaces

43. Complete Metric Spaces

45. Compactness in Metric Spaces

46. Pointwise and Compact Convergence

Chapter 9: The Fundamental Group

51. Homotopy of Paths

52. The Fundamental Group

53. Covering Spaces

54. The Fundamental Group of the Circle

55. Retractions and Fixed Points

56. * The Fundamental Theorem of Algebra