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Prospectus

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Advanced topics in analysis (TUD)

Course
2011-2012

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.

Literature
Lecture notes
Course code TUD
WI4211
Prerequisites
Some basic knowledge of functional analysis. Leiden’s Linear Analysis is more than sufficient.
Examination
Assignments and/or oral examination
Contact
2 hours per week
Remark
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.
Remark
This course can be part of a Leiden master programme

Links
Blackboard TU Delft
TU Delft study guide page