TOPOLOGY

MATH 4702/5702-001 -- SPRING 1999

Instructor:

Tolya Puhalskii

Office:

CU Building, Room 613

Phone:

303-556-4811

Email:

puhalski@math.cudenver.edu

Home page:

http://www-math.cudenver.edu/~puhalski/

Class hours:

Monday & Wednesday 2:00 p.m. - 3:15 p.m., 353 TR

Office hours:

Monday & Wednesday 4:00 p.m. - 5:00 p.m. (or by appointment).

Text:

C.W. Baker, Introduction to Topology, Krieger, 1997.
Interplay of various topological concepts is nicely illustrated in
Counterexamples in Topology, Dover, 1995, by L.A. Steen and J.A. Seebach,
which is, however, somewhat more advanced. Another good book that you might want to use is Topology, A First Course, by J.R. Munkres.

Course description.

We will cover core topics of point-set topology: topological spaces, separation axioms, separability, product-space topology, metric spaces, compactness and compactification, metrization, connectedness.

Course objectives.

My goal is that by the end of the course you have a clear understanding of the basic topological concepts, are able to use them for proving things, and appreciate importance of topology for other areas of mathematics.

Prerequisites.

There are no formal subject matter prerequisites. However, you will be missing much of the motivation for the concepts introduced unless you have studied some analysis. Also doing proofs is an integral part of the course, so, you should have enough mathematical maturity to pull this off; therefore, it will help if you have MATH 3000 behind you.

Homework.

Homework will be assigned regularly. Working problems is a crucial part of learning mathematics. No one can learn topology merely by pouring over the definitions, theorems and examples that are worked out in the text. You must work part of it out for yourself. There will be 7 homeworks. I will drop your two lowest scores.

Grading.

There will be one in-class mid-term and a take-home final exam. Homework will be given weight 30%, the midterm, 30%, and the final exam, 40%. The final grade will be based on the standard grading scale: 90%=A, 80%=B, 70%=C, 60%=D.

Dropping.

The final dropping date is February 3.

Incompletes.

Incompletes will only be given to students who are in good standing and are unable to finish the course for reasons beyond their control.