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INTRODUCTORY TOPOLOGY

### FALL 2008

### Basic information for Fall 2008

- Instructor: Professor E. Speer, Hill
Center 520, 732–445–1313, speer
*at* math *dot* rutgers
*dot* edu
- Office hours:
- Monday 1:40–3:00 PM, Hill 520
- Tuesday 3:20–4:40 PM, Hill 520
- Wednesday 10:20–11:40 AM, Hill 520
- Or by appointment or chance in Hill 520

- Detailed course information and policies:
As web page and as a PDF file.
- Hints on writing proofs:
- Homework assignments and solutions:
Click here for assignments and solutions.

### Final exam

The final exam is scheduled for **Friday, December
19, 12:00–3:00 AM,** in **ARC 110.**
- The exam is cumulative. It should be much like the midterms, although it may include a section of short answer problems.
- I will hold office hours
**Thursday, December 11, 10:30–12:00 AM**
**Thursday, December 18, 10:30–12:00 AM**
**Thursday, December 18, 3:00–4:30 PM**

- You are also welcome to look for me at any time in Hill 520. An
appointment is also possible, although I will be attending talks at the
Statistical Mechanics Conference and so we may have to schedule any meeting
rather tightly.

### Announcements and additional resources

- In our proof of the Urysohn lemma on November 24 one step was left as
an exercise, but I did promise to post details. Here is the verification of that step.
- Here is the class handout on the
relations among, and the heritability of, various coutability properties.
- Here is the promised brief writeup of the
**definition of a Lebesgue number** and **proof that every open cover
of a compact metric space has a Lebesgue number.**
- The book
*Counterexamples in Topology* is now on reserve in the
Hill Center Math Library.
- I regret that I must
**cancel my office hours for Tuesday, November
4**.
- My office hours on
**Monday, September 29**, are rescheduled from
**10:20 to 11:40 AM**.
- In case you would like to read more about set theory, I have placed on
reserve in the Math Library (in Hill Center) the book
*Naive Set
Theory*, by Paul Halmos. Its a well written, easy to read
introduction.
- A
"home page" for the Axiom of Choice.

### Exam 1

The first exam will be held **Wednesday, October 8**. It will cover
all our work through October 1; in particular, this includes all of Section
18 up to, but not including, Theorem 18.3. There is a homework
"Assignment" for the week of October 6, but it will not be collected.

### Exam 2

The second exam will be held **Wednesday, November 12**. As with the
first exam, it may ask you to state theorems or definitions from class or
the book, reprove results we proved in class or on homework, or answer
completely new questions.
The exam will cover our work through November 5, but there will not be any
questions dealing specifically with Chapter 1. We covered all of Chapter 2
except for Section 22; in Chapter 3 we covered most of Sections 23, 24, 25
through page 160, 26 up to the discussion of the finite intersection
property (bottom of page 169), 27, and 28. There is a homework
"Assignment" for the week of November 12, but it is for study purposes
only, and will not be collected.