Module Title
Topology

Module Level
Level 3

Module Credits
5.00

Academic Year
2024/25

Semester
SEM1

To introduce and illustrate the main ideas of topology by primarily building on material seen in MTH224 Metric Spaces as well as enhancing studentsâ€™ understanding of mathematics seen elsewhere (such as real and complex analysis, abstract algebra etc.) and providing a foundation to study further in the areas of geometry and topology.

A. Apply a variety of different techniques in point set, geometric and algebraic topology. B. Recognize a wide variety of topological spaces and their properties such as compactness and connectedness. C. Prove, or give counter-examples to, simple statements about topological spaces and continuous maps. D. Explain how to construct spaces by gluing and to prove in certain cases that the result is homeomorphic to a standard space. E. Distinguish topological spaces by means of invariants such as the fundamental group. F. Calculate the Euler characteristic of a triangulated surface and identify it with one listed in the classification theorem.

This module will be delivered through a combination of formal lectures and tutorials.