Prerequisites: Graduate standing.
This course builds on the basics of point-set topology and discusses topological spaces, continuity, connectedness and path-connectedness, compactness, product spaces, quotient spaces, metric spaces, countability and separation axioms. Further topics may include category theory and basic homotopy theory.
Outcomes: Students will strengthen their ability to read, understand, and communicate arguments about general topological spaces, preparing them for further advanced work in mathematics.
This course builds on the basics of point-set topology and discusses topological spaces, continuity, connectedness and path-connectedness, compactness, product spaces, quotient spaces, metric spaces, countability and separation axioms. Further topics may include category theory and basic homotopy theory.
Outcomes: Students will strengthen their ability to read, understand, and communicate arguments about general topological spaces, preparing them for further advanced work in mathematics.