# Topology

### 💬 Announcements

- Model solutions for the coursework problems
- The 📄 coursework paper is now available. You are encouraged to have a look at Manfred Lehn's valuable advice on how to work on problem assignments.
- Klein Bottle as a ✂ papercraft

### Background material

### Material organised by topics

#### Topological Equivalence [PDF]

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?

- Homework exercises, solutions will appear later at this place
- Quiz ✓

#### Topological Spaces [PDF]

Which data determines the topology of a subset of Euclidean space? How to generalise the idea of topological equivalence?- Homework exercises, solutions will appear later at this place
- Quiz ✓

#### Constructing New Spaces: Subspaces and Product Spaces [PDF]

How to construct new topological spaces out of existing ones?- Homework exercises, solutions will appear later at this place
- Quiz ✓

#### Constructing New Spaces: Quotient Spaces [PDF]

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

- Homework exercises, solutions will appear later at this place
- Quiz ✓

#### Hausdorff Spaces [PDF]

How to define the limit of a sequence in a topological space? How to ensure, that limit points are unique?- Homework exercises, solutions will appear later at this place
- Quiz ✓

#### Compactness [PDF]

How to generalise the Bolzano-Weierstraß Theorem to topological spaces?- Homework exercises, solutions will appear later at this place
- Quiz ✓

#### The Fundamental Group [PDF]

An*algebraic*invariant of topological spaces.

- Homework exercises, solutions will appear later at this place

#### The Fundamental Group of the Circle and Applications [PDF]

- Homework exercises, solutions will appear later at this place

### Weekly video lectures

All video lectures including the review sessions are also available on the video portal.

### Weekly in-class exercises

...will appear soon at this place.### Assessment and Feedback

#### Feedback

You will receive feedback on your understanding in this course- from the coursework
- during the tutorial
- from the online quizzes
- during my office hour, and
- via the generic feedback (and exam script viewing) on the final exam.

#### Coursework

Coursework paper 2021 [solutions] 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 online before 13:00 on 16 April 2021. The weighting of the coursework will be 20% of the final mark.#### Examination

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