- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Occurrence | Teaching period |
---|---|
A | Spring Term 2022-23 |
To introduce the theory of abstract topological spaces and their properties.
To introduce the notion of a topological invariant and study fundamental ones such as connectedness, compactness and that of being Hausdorff.
To introduce the notion of homotopy and simply connected with a view to demonstrating why two spaces are not homeomorphic.
Subject content
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.
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
[Pre-requisite modules: students must either have taken Pure Mathematics or Pure Mathematics Option 1.]
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 undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
J. Munkres, Topology 2ed., Prentice Hall 2000