The following list, which will continue to be updated, contains more precisely
what I expect you to have learned. It is expected that you study on your own those parts
below which are not covered in the lectures.

For the exam, you are supposed to know all the definitions, theorems and proofs as described below as well as
be able to apply these things.

Part I  (general/ point-set topology)

1. All exercises listed in the exercise link, both those which I plan to present as well as the others.

2. Zorn's lemma and the relevant definitions at the end of Section 11.

3. Section 12.

4. Section 13 with the exception of Lemma 13.2. The notion of a subbasis might come up in some later
proof but otherwise we won't deal with it.

5. Section 15 with the exception of Theorem 15.2.

6. Section 16 up to and including Theorem 16.3.

7. Section 17 with the exception of the proof of Theorem 17.4 and Theorem 17.11.

8. Section 18 with the exception of the proof of Theorem 18.1

9. Section 19 with the exception of the discussion about subbases and Theorem 19.5.

10. Section 20.

11. Section 21 with the exception of the proof of Theorem 21.3.

12. Section 23 with the exception of Lemma 23.1.

13. Section 24  with the exception of Theorem 24.1 (which will be replaced by a direct proof of Corollary
24.2) and Example 6.

14. Section 25 but only pages 159-160.

15. Section 26.

16. Section 27 with the exception of Theorem 27.1 (which will be replaced by a direct proof of Corollary
27.2). (The Lebesgue number lemma will be needed when we do the second half of the course.)

17. Section 28 but only the statement of Theorem 28.2 as well as the example presented in class of a compact
space which is not sequentially compact.

18. Section 30 but only pages 190-191.

19. Section 31 but only pages 195-197.

20. Section 32 but only Theorems 32.1-32.3.  For 32.1, just the statement.

21. Section 33 but only the statement of Urysohn's lemma as well as a proof of the result for
metric spaces.

22. Section 34 but only the statement of the Urysohn metrization theorem as well as
the slightly simpler proof for compact spaces which I will present in class.

23. Section 35.

24. Section 37.

25. Section 43.  Just until the middle of page 65. The rest of the section can be replaced (for our purposes)
by a proof (which I will do in class)  that the continuous functions on the closed interval 0,1  (in the uniform
metric) is a complete metric space.

26. Section 44.

27. Section 45. Just first two pages.

28. Section 48. Up to but not including Lemma 48.4.

29. Section 49.


Part II  (algebraic topology)


30. Section 22.  Everything except Theorem 22.1 and Examples 6 and 7.

31. Section 51.  Everything.

32. Section 52.  Everything.

33. Section 53.  Everything.

34. Section 54.  Everything up to but not including Theorem 54.6.

35. Section 55.  Everything except (a) the proof of 3 implies 1 in Lemma
55.3 and (b) everything after the proof of Theorem 55.6.

36. Section 57.  Everything except the proof Theorem 57.1.

37. Section 58. Only statement of Theorem 58.3 and corresponding needed
definitions and applications on page 362.

38. Section 60. Everything.

39. The four notes written by me on the homepage.
(a) Group actions, part 1, (b) group actions, part 2
(c)semi-direct products and (d) Fundamental group of the Klein bottle.