This is a course in point-set topology. Concepts of point-set topology extremely important and underlie much of modern mathematics. Topics developed in this course are widely used in many areas of study. Topics will be selected from the following:
- Sets, Functions Notation
- Metric Spaces (Generalization of the notion of distance)
- Continuity
- General Topological Spaces
- Basic Constructions: New Spaces From Old
- Separation Axioms
- Compact Spaces
- Locally Compact Spaces
- Connected Spaces
- Other Types of Connectivity
- Continua
- Homotopy
Prerequisites.
MATH 220 and some experience writing mathematics and proving theorems.
Textbook:
Topology by Sheldon W. Davis, McGraw-Hill, 2005.
Grading Course grades will be determined by one midterm, one final
and homeworks (33.3% each).
This course combines honors and standard tracks. Homeworks will be given weekly and contain *-problems.
Regular students are welcome to attempt these problems for extra credit.
Honors track students are expected to attempt as many the *-problems as they can.
Homework
Homework 1 Due: 1/24
Homework 2 Due: 1/31
Homework 3 Due: 2/7
Homework 4 Due: 2/14
Homework 5 Due: 2/21
Homework 6 Due: 2/28
Homework 7 Due: 3/20
Midterm: In class March 6.
Material to prepare for midterm
Homework 8 Due: 3/27
Homework 9 Due: 4/3
Homework 10 Due: 4/10
Homework 11 Due: 4/24
Final: Friday, December 7, 12:30-2:30 pm
Material to prepare for final