Math 440/540 Homework
from Introduction to Topology 2^nd Edition,
by Gamelin & Greene

Chapter 1

1.1: 1,2,5–14

Supplementary Exercises 1

1.2: 6,7,8
1.3: 9 [note 9(c) has a mistake, should be m,n integers (not necessarily positive) ]
1.4: 4,7
1.5: 1,2,5,7
1.6: 1,2,3,7,10

Sections 1.2-6 will not be turned in. They are more related to analysis than topology. You should take a look at the problems to get a feel for what is there. Take a look at the construction in problem #7 of 1.2. It is fundamental. Also of note is the characterization of compactness in a general metric space as those sets which are closed and totally bounded. This differs from classification of compact subsets in euclidean space as closed and bounded (a weaker condition than total boundedness).

Supplementary Exercises 2

Chapter 2

2.1: 1–9,12
2.2: 2
2.3: 2,3,4,5,6,7,11,14
2.4: 1–3,5,7,8 (see back of book for mistake in #8)
2.5: 1–3,5,7,9
2.6: 1–4,6 (look at #7)
2.7: 1–4
2.8: 1,3,4,6,8–11
2.9: 2–5 (look at 7,8)
2.10: 1,2,4
2.12: 10,11
2.13: 1,2,3,8

Supplementary Exercises 3

Chapter 3

3.2: 1,5
3.3: 1–9
3.4: 1–3
3.5: 1–6 (we may be able to do 7–11 in class)