Topology and Advanced Analysis (803G1)

15 credits, Level 7 (Masters)

Autumn teaching

Topics that will be covered in this module include:

  • Topological spaces
  • Base and sub-base
  • Separation axioms
  • Continuity
  • Metrisability
  • Completeness
  • Compactness and Coverings
  • Total Boundedness
  • Lebesgue numbers and Epsilon-nets
  • Sequential Compactness
  • Arzela-Ascoli Theorem
  • Montel's theorem
  • Infinite Products
  • Box and Product Topologies
  • Tychonov Theorem
  • Banach-Alaoglu theorem.


100%: Lecture


20%: Coursework (Problem Set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is 150 hours of work. This breaks down into 33 hours of contact time and 117 hours of independent study.

This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.