Hendrik Süß
Hendrik Suess

# Topology (MATH31052)

Please try to watch the podcasts early in the week (say up until Wednesday). They are meant to complement the notes. Have a go at the inclass-problems. They are posted on this website and additionally on the discussion board. Make use of the discussion board: discuss the problems, suggest solutions, discuss your attempts and difficulties. On Friday during the online tutorial I will assume that you have read the questions and attempted the problems.

### 💬 Announcements

• The coursework has been marked. You can find your mark on Blackboard. Individual feeback is given via Turnitin. Solutions and generic feedback can be found here.
• Week 9
Fundamental Group, Applications (Brouwers Fixed Point Theorem)
Week 10
The Fudamental Group of the Circle
Week 11
Applications (Fundamental Theorem of Algebra), Revision
Week 12
Revision
• Important The deadline for coursework submissions has been pushed back by one week. The new deadline is 13:00 Friday 27 March.

### Course topics

#### 1. Topological Equivalence

What is Topology? When are two subsets of Euclidean space equivalent from the view point of topology? How to check that two subsets are or are not topologically equivalent?

#### 2. Topological Spaces

Which data determines the topology of a subset of Euclidean space? How to generalise the idea of topological equivalence?

#### 3. Constructing New Spaces: Subspaces and Product Spaces

How to construct new topological spaces out of existing ones?

#### 4. Constructing New Spaces: Quotient Spaces

Is there a natural topology on the set of equivalence classes of a topological space?

#### 5. Hausdorff Spaces

How to define the limit of a sequence in a topological space? How to ensure, that limit points are unique?

#### 6. Compactness

How to generalise the Bolzano-Weierstraß Theorem to topological spaces?

#### 7. The Fundamental Group

An algebraic invariant of topological spaces.

### Weekly in-class exercises

Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12,

### Assessment and Feedback

#### Feedback

1. from the coursework
2. during the tutorial
3. from the online quizzes
4. during my office hour, and
5. via the generic feedback (and exam script viewing) on the final exam.

#### Coursework

The coursework is a take-home test. Starting from week 5 you will find the questions in the following PDF document.

You are encouraged to have a look at Manfred Lehn's valuable advice on how to work on problem assignments.

The solutions have to be submitted via Blackboard/TurnitIn before 13:00 on Friday 27 March. The weighting of the coursework will be 20% of the final mark.

#### Examination

The format of the exam paper will be the same as in the last year, but different from previous years. There will be one section with six mandatory questions.

Solving the homework exercises is meant as an effective preparation for the exam. You might also have a look at the past papers below.

Past papers + feedback: 2016/17, 2017/18

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School of Mathematics
The University of Manchester
Alan Turing Building
Manchester M13 9PL

1.106a

#### contact:

Phone: +44 161 275 5818
email:
hendrik.suess@manchester.ac.uk

Mon 10:30-11:30