Math 5801: General Topology and Knot Theory

In topology, we study geometric objects with an emphasis not so much on the size of things, but rather on those properties of spaces which are preserved under continuous deformations.

In this course in particular, we focus on:

• general topology or “point-set topology” which establishes the foundations of metric spaces and topological spaces and the so-called big C’s of continuity, convergence, connected- ness, compactness, countability; and
• knot theory which studies embeddings of circles in three-dimensional space through com- binatorial, geometric, and algebraic techniques and invariants.

This course is a fast-moving journey through point-set topology, suitable for someone who has had some experience with a proof-based math course and is ready to dive into some naïve set theory today.