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Topology - MAT00044H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Jason Levesley
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2021-22
    • See module specification for other years: 2022-23

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Module will run

Occurrence Teaching period
A Spring Term 2021-22

Module aims

  • 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.  

Module learning outcomes

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

  • 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.]

Assessment

Task Length % of module mark
Online Exam -less than 24hrs (Centrally scheduled)
Topology		 2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
Online Exam -less than 24hrs (Centrally scheduled)
Topology		 2 hours 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


The information on this page is indicative of the module that is currently on offer. The University is constantly exploring 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 by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.