Topology and Advanced Analysis
Module code: G1026
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination
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
- 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.
Module learning outcomes
- Understand the concepts of a topological space, open and closed sets and interior and closure.
- Understand the concept of a metric and a metrisable topology.
- Understand and manipulate coverings, continuity and compactness.
- Understand Arzela-Ascoli theorem and some of its basic consequences.