15.4 c)
20.1, 20.2, 20.7 b) implies c) and c) \implies d)
22.5
23.2, 23.3
24.1, 24.2, 24.3, 24.4, 24.10
25.1, 25.2
26.1, 26.3, 26.10, 26.11, 26.15
27.1, 27.2, 27.7, 27.9
28.2, 28.5, 28.6, 28.9, 28.12 b), 28.13
29.1, 29.2, 29.3, 29.4, 29.7
Theorem 1 from
``Notes for October 27''
30.2
32.1, 32.6, 32.9
33.1
35.1, 35.2, 35.3 b), 35.5
36.1, 36.2 before the ``Conversely''
42.1, 42.8, 42.10 b) assuming part a)
43.1, 43.12
See class notes for alternative proofs of 26.15, 27.9, 28.12 b), 30.2,
and especially 28.2 and 28.9.
You are also expected to know the definition of a Cauchy filter, and to be able to prove that every 0-dimensional compact metric space is homeomorphic to a subset of a countable product of discrete spaces.
Also there are some exercises that were for homework, which you could be asked to do (see below) and also Problem 28B3, which was done in class.
9. Show that every regular, paracompact space is normal.
12. Show 20B1, page 152.
20. Show 27B2, page 202.
24. The epsilon-balls of a non-Archimedean metric space partition the space into (cl)open sets. (In other words, any two epsilon-balls either coincide or are disjoint.)
30. Do exercise 35A, parts 1 and 4.