
Math 5853  001 Topology I
Fall 2010
Course Handouts and Messages
 The textbook for this course is Topology (2nd ed.) by James
R Munkres. We will work through as much of Part I (General Topology)
as possible this semester. Topology II in Spring 2011 will cover
topics from Part II (Algebraic Topology). We will also work from chapters 0 and
1 of Algebraic
Topology by Allen Hatcher in the Spring 2011 semester.
 Summer 2010 study plan. Read through as much as chapters 1 and
2 as you can. It is important to make sure you know about the typcial
material from a discrete mathematics (or foundations) course: sets,
subsets, power sets, cartesian products, functions, preimages and images of
subsets under functions, order
relations, equivalence relations, equivalence classes, partitions,
finite and infinite sets, countable versus uncountable sets.
Reals and integers, well ordering and induction, principle of recursive
definition.
You can find a detailed treatment of these topics in Chapter 1 of the text
book.
 Summer 2010 study plan. You should also review the notion of
a continuous function (as defined in the Calculus sequence or in a
foundations or analysis class). If you have seen the notion of a metric
space, you could review that too. Don't worry if you have not met this
concept. We will treat it in detail in the Fall semester.
 Information Sheet. First week handout.
 Here are some sample questions for mid I.
 Solutions to the midterm exam.
 The (p,q)torus knot homework can be simplified using the following two
useful lemmas. The second lemma uses the following
interesing fact about quotient spaces. The
scanning process seems to have darkened the following
figure in the latter handout.
 Here are copies of my old topology qualifying examinations
from Spring 2003
and Summer 2003.
You can look here
for other qualifying examinations.
 Here is a final examination from Fall 2002.
 You only have to turn in (1) through (9) of the (p,q)project. You should
do so by Monday afternoon (3pm). I will post solutions here once I have
all the scripts.
Homework
 [01]. Due Friday 08/27. Turn in starred problems.
Pages 1415: 5*, 7*, 8, 9
Pages 2021: 1*, 2
Pages 2829: 2*, 4, 6, 7, 12*.
 [02]. Due Friday 09/03. Turn in starred problems.
Page 39: 4*, 5
Page 44: 3*, 5, 6, 7
Pages 5152: 3, 4, 5*, 6*, 7
Page 56: 8

[03]. Due Friday 09/17. Write out the details of Proof 8
and Proof 25 from the "Well ordered sets, ordinals" handout.
Write out the details of the circle of implications in Proof 8
of the "Axiom of choice, etc" handout.
Do exercise 11 of the "Axiom of choice,..." handout.
I'll give the Axiom of choice handout to you in class on Monday.

[04]. Due Monday 10/04. Page 83: 6,7
Page 92: 2, 4, 5, 10
Page 101: 6, 7, 9, 10, 11, 12, 13, 15, 21
Do this problem. There is a small typo
in the pdf, $n \in Z \{0\}$ should read $n \in Z^+ \{0\}$.

[05]. Due Monday 10/18.
Pages 14445: 2, 3*, 4, 6*
Pages 11112: 2*, 4, 8*, 12, 13*
Page 118: 1, 2, 3, 4*, 5, 6*, 7*

[06]. Due Monday 11/08.
Page 152: 1*, 5*, 7, 8, 10, 11*
Pages 15859: 4*, 5, 8, 9*, 10*, 12
Pages 16263: 3, 4, 5*, 8*

[07]. Due Wednesday 11/17:
Pages 17072: 3*, 4*, 5*, 6, 7, 8
Pages 17778: 1, 3*, 4, 6
Pages 18182: 6*, 7

[08]. Due Monday 11/22:
Do the following exercises from the Cones, Suspensions,
Joins handout:
6, 9, 11, 13, 14, 16, 17, 18 (or 19, your choice).
 [09]. Starred are
due by last day of class: Pages 19495:
2, 4, 5*, 6*, 7, 11*, 12, 14
Pages 199200: 1*, 3, 6*, 7
Pages 20507: 1*, 2*, 3*, 4, 7, 8, 9
 Project. Turn in the (p,q)torus knots
project by the last day of class.
