MA32056: Introduction to topology
[Page last updated: 22 May 2025]
| Academic Year: | 2025/26 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Honours (FHEQ level 6) |
| Period: |
- Semester 2
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| Assessment Summary: | EXCB 100% |
| Assessment Detail: |
- Closed-book written examination (EXCB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you are advised to take MA22032 OR take MA20218
In taking this module you cannot take MA30055
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| 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.
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| 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.
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| 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.
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| Course availability: |
MA32056 is Optional on the following courses:
Department of Computer Science
- USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
- USCM-AFM32 : MComp(Hons) Computer Science and Mathematics (Year 3)
- USCM-AKM32 : MComp(Hons) Computer Science and Mathematics with professional placement (Year 3)
- USCM-AKM32 : MComp(Hons) Computer Science and Mathematics with study abroad (Year 3)
Department of Mathematical Sciences
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB30 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFM30 : MMath(Hons) Mathematics (Year 3)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
Department of Physics
- USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
- USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 3)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)
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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.
- 好色tv and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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