Topology and Advanced Analysis (G1026)

15 credits, Level 6

Autumn teaching

This module will introduce you to some of the basic concepts and properties of topological spaces. The subject of topology has a central role in all of Mathematics and having a proper understanding of its concepts and main theorem is essential as part of an undergraduate mathematics curriculum.

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. 

Teaching and assessment

We’re currently reviewing teaching and assessment of our modules in light of the COVID-19 situation. We’ll publish the latest information as soon as possible.

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

This module is running in the academic year 2020/21. 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.

Courses

This module is offered on the following courses: