Point Set Topology

(3 Credit Hours) · Undergraduate

The course will introduce the basic concepts of topology as well as some key questions and techniques in the subject. Topics to be covered will include: metric spaces; compact, complete and Hausdorff spaces; cell complexes; deformation retractions; homotopy equivalent spaces. Additional topics may include: fundamental groups and van Kampen's theorem; covering spaces and deck transformations; higher homotopy groups; manifolds; handlebodies and Heegaard splittings; Euler characteristic; space-filling curves; the Brouwer fixed-point theorem, among others.