Topology - MAT00044H
- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Related modules
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Spring Term 2022-23 |
Module aims
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To introduce the theory of abstract topological spaces and their properties.
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To introduce the notion of a topological invariant and study fundamental ones such as connectedness, compactness and that of being Hausdorff.
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To introduce the notion of homotopy and simply connected with a view to demonstrating why two spaces are not homeomorphic.
Module learning outcomes
Subject content
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Fundamental abstract notions of general topology including topological spaces, continuous maps, subspaces, connectedness, compactness, homeomorphisms, and examples of separation properties. Basic examples of topological spaces, particularly “non-Euclidean” ones.
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Homotopies of maps, homotopy equivalence and simply connectedness of a space as a topological invariant. Understand that the sphere is simply connected, but the torus is not.
Academic and graduate skills
- Develop the ability to think abstractly about mathematics learnt in the first two years of the mathematics programme, particularly in calculus and analysis. Understand the fundamentals of topology for those who wish to continue further study in pure mathematics.
Module content
[Pre-requisite modules: students must either have taken Pure Mathematics or Pure Mathematics Option 1.]
Indicative assessment
| Task | % of module mark |
|---|---|
| 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 undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
J. Munkres, Topology 2ed., Prentice Hall 2000