Topology - MAT00082H
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
Additional information
Metric Spaces (from 2024/25 onwards)
The M-level version of the module cannot be taken if H-level was taken.
Module will run
Occurrence | Teaching period |
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A | Semester 1 2025-26 |
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:
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Describe fundamental examples of topological spaces and analyse their properties.
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Use basic topological invariants such as connectedness, compactness and Hausdorff to study and distinguish spaces.
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Use homotopies of paths and the fundamental group to analyse the structure of spaces.
Module content
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Topological spaces and examples: Euclidean (or usual) topology, metric spaces, profinite and Zariski topologies.
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Topological invariants and fundamental examples: connectedness, compactness.
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Subspaces, product spaces and quotient spaces.
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Homotopies and the fundamental group.
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Knots and their invariants
Indicative assessment
Task | % of module mark |
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Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
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