## Topology

Module Title Topology
Module Level Level 3
Module Credits 5.00

#### Aims and Fit of Module

`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.`

#### Learning outcomes

```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.```

#### Method of teaching and learning

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