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# Topology - MAT00082H

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• Department: Mathematics
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2024-25
• See module specification for other years: 2023-24

## Module summary

This module is an introduction to topology - the abstract study of spaces and their properties. The central idea is that of a topological invariant.

## Related modules

• None

• None

### Additional information

Metric Spaces (from 2024/25 onwards)

## Module will run

Occurrence Teaching period
A Semester 1 2024-25

## Module aims

This module is an introduction to topology - the abstract study of spaces and their properties. The central idea is that of a topological invariant.

## Module learning outcomes

By the end of the module, students will be able to:

1. Describe fundamental examples of topological spaces and analyse their properties.

2. Use basic topological invariants such as connectedness, compactness and Hausdorff to study and distinguish spaces.

3. Use homotopies of paths and the fundamental group to analyse the structure of spaces.

## Module content

• Topological spaces and examples: Euclidean (or usual) topology, metric spaces, profinite and Zariski topologies.

• Topological invariants and fundamental examples: connectedness, compactness.

• Subspaces, product spaces and quotient spaces.

• Homotopies and the fundamental group.

## Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

None

### Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

## Indicative reading

M A Armstrong, Basic Topology, Springer UTM.

James Munkres, Topology: a first course, Pearson

Allen Hatcher, Algebraic Topology, Cambridge University Press

The information on this page is indicative of the module that is currently on offer. The University constantly explores ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.