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MA30356: Introduction to topology

[Page last updated: 22 May 2025]

Academic Year: 2025/26
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 2
Assessment Summary: EXCB 100%
Assessment Detail:
  • MA32056 Closed-book written examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA22032 OR take MA20218
In taking this module you cannot take MA30055
Learning Outcomes: By the end of this unit, you will be able to:
  • Demonstrate familiarity with topological spaces and explain their role in topology, analysis and geometry.
  • Demonstrate an understanding of compactness and connectedness in this general setting.
  • Apply topological ideas and methods to examples.



Synopsis: Topology is concerned with properties that are preserved by continuous maps. This is not an analysis course, although it starts from analysis: some of the ideas will be more familiar from algebra, but topology is different from both. You will learn how to make statements such as "there is no difference between a doughnut and a coffee cup" precise, and you will see the classification of surfaces, including non-orientable surfaces such as the Klein bottle.

Content: Topologies and topological spaces, continuous maps and homeomorphisms, subspaces, product spaces, quotient spaces, compactness and connectedness. Further topics will be chosen from: function spaces and compact-open topologies; Hausdorff spaces and separation axioms; Tychonoff's theorem; Compact surfaces, their representation as quotient spaces, and a sketch of their classification.

Course availability:

MA30356 is Optional on the following courses:

Department of Mathematical Sciences
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
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