This course is on the topology of function spaces. We begin with an introduction to General Topology, with emphasis on separation axioms and compactness. After that we will consider various topologies on sets of continuous functions: the pointwise, compact-open and uniform topologies. Our goal is to prove the Arzela-Ascoli theorems that characterize compactness in certain function spaces. We will end with a few applications: to differential equations and the Riemann mapping theorem.
Course code TUD
Some basic knowledge of functional analysis. Leiden’s Linear Analysis is more than sufficient.
Assignments and/or oral examination
2 hours per week
There is some overlap with the Leiden second year Topology course. Please contact the lecturer beforehand about the number of EC to be awarded if you have taken that course.
This course can be part of a Leiden master programme