Topology and Advanced Analysis (L6) (G1026)
Topology and Advanced Analysis (L6)
Module G1026
Module details for 2022/23.
15 credits
FHEQ Level 6
Module Outline
The aim of this module is to provide an introduction to important topological concepts, and to explain how these can be applied in Analysis.
The module discusses the definition of topology, and how this allows to introduce continuous functions and homeomorphisms.
The comparison between different topologies is also studied.
Then, the relation between metric and topological spaces is considered.
The fundamental concept of compactness is introduced, and the relation between different kinds of compactness is discussed.
Applications to the case of function spaces are then studied.
The module will include:
• Topological spaces
• Metric spaces
• Compactness
• Equivalence of several compactness notions in metric spaces
• Arzelà -Ascoli Theorem
• Tychonoff Theorem
Module learning outcomes
Gain a coherent and detailed knowledge of the concepts of a topological space and open and closed sets and interior and closure.
Systematically understand the concept of a metric and a metrisable topology.
Be able to use and have a coherent knowledge of the concepts of coverings, continuity and compactness.
Systematically understand Arzelà -Ascoli theorem and some of its basic consequences.
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 8.00% | |
| Coursework components. Weighted as shown below. | ||
| Portfolio | T1 Week 11 | 100.00% |
| Unseen Examination | Semester 1 Assessment | 80.00% |
| Coursework | 12.00% | |
| Coursework components. Weighted as shown below. | ||
| Problem Set | T1 Week 4 | 25.00% |
| Problem Set | T1 Week 6 | 25.00% |
| Problem Set | T1 Week 9 | 25.00% |
| Problem Set | T1 Week 11 | 25.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Semester | Lecture | 1 hour | 11111111111 |
| Autumn Semester | Lecture | 2 hours | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Prof Ali Taheri
Convenor, Assess convenor
/profiles/203434
Dr Miroslav Chlebik
Convenor, Assess convenor
/profiles/202996
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