- Department: Mathematics
- Credit value: 20 credits
- Credit level: H
- Academic year of delivery: 2023-24
- See module specification for other years: 2024-25
This module is an introduction to topology - the abstract study of spaces and their properties. The central idea is that of a topological invariant.
Pre-requisite modules
Co-requisite modules
Prohibited combinations
- None
Metric Spaces (from 2024/25 onwards)
Occurrence | Teaching period |
---|---|
A | Semester 1 2023-24 |
This module is an introduction to topology - the abstract study of spaces and their properties. The central idea is that of a topological invariant.
By the end of the module, students will be able to:
Describe fundamental examples of topological spaces and analyse their properties.
Use basic topological invariants such as connectedness, compactness and Hausdorff to study and distinguish spaces.
Use homotopies of paths and the fundamental group to analyse the structure of spaces.
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.
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 100 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
M A Armstrong, Basic Topology, Springer UTM.
James Munkres, Topology: a first course, Pearson
Allen Hatcher, Algebraic Topology, Cambridge University Press