Hendrik Süß

# Topology

### Background material

A topological surface of genus 4

### 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?

#### Topological Spaces[PDF]

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

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

How to construct new topological spaces out of existing ones?

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

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

#### Hausdorff Spaces[PDF]

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

#### Compactness[PDF]

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

#### The Fundamental Group[PDF]

An algebraic invariant of topological spaces.

### 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

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

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.

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

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Friedrich-Schiller-Universität Jena
Institut für Mathematik

Ernst-Abbe-Platz 2
07743 Jena

3527

#### Erreichbar unter:

Telefon: +49 (0) 3641 946165
Email: hendrik.suess@uni-jena.de