Frequency:

Fall/Spring

Student Body:

Math majors and graduate students in related areas

Background and Goals:

This is an introduction to the basic ideas and methods of point set topology. It is a good background for analysis courses and graduate topology courses. Normally it is advisable to have at least one previous proof-based course such as Math 341, Math 421, Math 521 or Math 541 before taking Math 551.

Alternatives:

N/A

Subsequent Courses:

Math 552.

Course Content:

- Elementary Set Theory: Sets, Cartesian products, equivalence relations, countability, the real line
- Basic Topology: metric spaces, topological spaces, basis, continuity, connectedness, compactness
- Selected Topics: Product and quotient topologies, manifolds, normality and extension theorems, the fundamental group, covering spaces

credits:

3. (N-A)

semester:

FallSpring

prereqs:

MATH 341, 375, (MATH 421 and 320), (MATH 421 and 340), (MATH 521 and 320) or (MATH 521 and 340) or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) Program