## Availabilities:

Not currently available in 2019

## Unit Summary

### Unit type

UG Coursework Unit

12

7

### Former School/College

Former School of Education

### Pre-requisites

have completed MAT10722 - Complex Analysis

## Unit aim

Introduces the concept of topology and its applications. The course includes topological spaces and related constructions and properties, connectedness and its applications, as well as compactness and related properties.

## Unit content

Complex Analysis (Topics 1 to 5)
1. Theory of sets – sets and operations
2. Theory of sets – functions and relations
3. Metric spaces – metric spaces and continuity
4. Metric spaces – limits, open and closed sets, subspaces and equivalence
5. Topological spaces – spaces and functions
6. Topological spaces – subspaces, products, identification topologies
7. Connectedness – introduction and applications
8. Connectedness – components and local connectedness, path-connected spaces
9. Compactness – compact topological spaces, subsets and products
10. Compactness – compact metric spaces, Bolzano-Weierstrass property, surfaces by identification

## Learning outcomes

Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.

On completion of this unit, students should be able to:

1. correctly use concepts and techniques of topology in known contexts
• GA1:
• GA4:
2. correctly apply concepts and techniques of topology to new contexts
• GA1:
• GA2:
• GA4:
3. effectively communicate mathematical ideas, processes and results at different levels of formality
• GA1:
• GA4:
• GA6: