Topology and Advanced Analysis (L7) (803G1)
Topology and Advanced Analysis (L7)
Module 803G1
Module details for 2023/24.
15 credits
FHEQ Level 7 (Masters)
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
Comprehensively understand and manipulate the concepts of a topological space, open and closed sets and interior and closure.
Systematically understand the concept of a metric and a metrisable topology.
Be able to work with and understand the concepts of coverings, continuity, homeomorphism and compactness.
Comprehensively understand Arzelà -Ascoli theorem and some of its consequences.
| Type | Timing | Weighting |
|---|---|---|
| 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% |
| Coursework | 8.00% | |
| Coursework components. Weighted as shown below. | ||
| Portfolio | T1 Week 11 (1 hour) | 100.00% |
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
Assess convenor, Convenor
/profiles/202996
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