MCS 332: Topology
Spring 2002
Catalog description
An introduction to the techniques and theorems of basic pointset
topology. Topics will include: countability and separation axioms,
Urysohn's lemma, compactness, connectedness, and product spaces.
Optional topics may be covered from other areas in analysis and
topology.
Prerequisite: MCS 331 (Real Analysis)
Instructor: John Holte
Office: Olin 307
Office hours: M 1:302:20, TR 10:3011:20, F 1:302:20
and when my door is open.
Telephone: x7465
Email: holte@gac.edu
Note: There is no "j" in my email address.
Homepage: http://www.gac.edu/~holte/
Textbooks
 Required: Topology, second edition, by James R. Munkres,
Prentice Hall, Upper Saddle River, NJ, 2000.
 Recommended: Counterexamples in Topology
by Lynn Arthur Steen and J. Arthur Seebach,
Dover Publications, New York, 1978.
Class meetings

We'll meet at 10:30 Monday, Wednesday, and Friday each week.

Faithful attendance is expected.
 Excuses: Talk to me in person regarding excused
absences. Do not expect mailed, email, or voicemail messages to
count.
Course web page
Chapter
 Topics
 Exam

1
 Set theory and logic


2
 Topological spaces and continuous functions
 Mar. 1518

2
 Finish ch. 2


3
 Connectedness and compactness
 Apr. 1922

4
 Countability and separation axioms


5
 The Tychonoff theorem


7
 Complete metric spaces and function spaces
 May 1720

16, 7
 Wrapup and review
 Fri., May 24
3:305:30

Exams
There will be three unit exams and a comprehensive final exam.
The exams will have two parts: a closedbook inclass part
and an openbook takehome part.
The best three will be counted.
You may opt not to take the final exam if you are satisfied with
your performance on the the three unit exams.
The tentative schedule of exams is given in the
syllabus.
You learn mathematics by doing mathematics.
Accordingly, you may find that doing the homework is the most
instructive part of the course. You may discuss issues related to
assigned problemsin fact, I encourage discussionbut when it comes
to the solution writeup, you must do that on your own.
Please observe the following rules.
 Acknowledge your sources (people and texts).
 In nontrivial problems, show how you get your answers.
 Turn in neat, wellwritten solutions, not messy first drafts.
Trim "fringes."
 Do not copy another's solutions; write up solutions in your own
words.
 Write proofs in good textbook style.
 Do extra credit problems entirely on your own.
Participation and presentations
Part of the time this course will be run as a seminar
in which we all are engaged in helping the others to a better
understanding of topology. Accordingly, sometimes you will be called
upon to present problem solutions or proofs of theorems in class.
Fraction
 Work
 Notes

1/3
 Problem assignments


1/2
 Exams
 You will have three unit exams and a comprehensive final.
The best three will be counted @ 1/6 each.

1/6
 Participation & formal presentations


Academic honesty
Page 68 of the Gustavus Guide
states in part: "The faculty of Gustavus Adolphus College expects all
students to adhere to the highest standards of academic honesty... In
all academic exercises, examinations, papers, and reports, students
shall submit their own work. Footnotes or some other acceptable form of
citation must accompany any use of another's words or ideas."
A first case of cheating will result in a zero on the test or
assignment in question.
A second case will result in a failing grade for the course
and be reported to the academic administration.
Extra help
I encourage you to see me during my office hours or at other times
when my office door is open.
Useful course information will also be maintained on the course webpage.
In addition, some course materials and problem solutions will be kept
in a notebook at Olin 307.
If you have a disability that requires an accommodation, please tell
me privately as soon as possible.