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