Introduction to topology (foundations, examples, fundamental theorems and introduction to the fundamental group and covering theory).
Roughly every two weeks, in the first part of the exercise classes, there will be a multiple choice quiz.
Depending on performance over all quizzes, students may get a 0.25 bonus on the final grade.
For students unable to attend the exercise classes, we will publish here the quiz around 10 AM.
Please submit your answers to your respective TA by email no later than 2 PM. If you are not registered
for an exercise class, you can submit to the course coordinator.
Here is the April 15 quiz.
Here is the April 29 quiz.
Here is the May 13 quiz.
Here is the May 27 quiz.
The exercise sheets will be posted on the homepage on Wednesday, starting with the first week of lectures. The solutions are posted usually on Thursday after the due date.
Please submit your solutions on SAMup by the following Wednesday.
exercise sheet | due by | upload link | solutions |
---|---|---|---|
Serie 1 | February 28 | Submission | Solutions |
Serie 2 Serie 2 (EN) | March 6 | Submission | Solutions |
Serie 3 Serie 3 (NEW) | March 13 | Submission | Solutions |
Serie 4 Serie 4 (EN) | March 20 | Submission | Solutions |
Serie 5 Serie 5 (EN) | March 27 | Submission | Solutions |
Serie 6 Serie 6 (EN) | April 10 | Submission | Solutions |
Serie 7 Serie 7 (EN) | April 17 | Submission | Solutions |
Serie 8 Serie 8 (EN) | April 24 | Submission | Solutions |
Serie 9 Serie 9 (EN) | May 1 | Submission | Solutions |
Serie 10 Serie 10 (EN) | May 8 | Submission | Solutions |
Serie 11 Serie 11 (EN) | May 15 | Submission | Solutions |
Serie 12 Serie 12 (EN) | May 22 | Submission | Solutions |
Serie 13 Serie 13 (EN) | May 29 | Submission | Solutions |
Serie 14 Serie 14 (EN) |
Day | Content |
---|---|
19.2.2024 |
Chapter I
Introduction to the course. Chapter 1, Introduction |
23.2.2024 |
Chapter II
Definition of topological spaces and continuous maps. Examples of topological spaces and continuous maps (euclidian spaces, subspaces, discrete topology, metric spaces, topological manifolds). Chapter 2, Topological spaces (Sections 1 to 3, with definition of topology of pointwise convergence corrected) |
26.2.2024 |
Examples of topological spaces and continuous maps
(Cantor space, function spaces, topological groups).
Chapter 2, Topological spaces (Sections 1 to 3, with definition of topology of pointwise convergence corrected) |
1.3.2024 |
Definition of a basis for a topology, of fundamental
systems of neighborhoods of a point; examples. Closure,
interior, boundary. Dense subsets. Examples.
Chapter 2, Topological spaces (Sections 4 to 6, with page 23 corrected) |
4.3.2024 |
Convergence of sequences, examples. Hausdorff spaces.
Chapter 2, Topological spaces (Sections 4 to 6, with page 23 corrected) |
8.3.2024 |
Filters.
Chapter III First discussion of compactness, connectedness and completeness. Chapter 2, Topological spaces (Sections 4 to 6) and Chapter 3, Section 1 (beginning). |
11.3.2024 |
Corrected definition of topology of pointwise
convergence. Compactness.
Chapter 3, Section 1 (beginning). |
15.3.2024 |
Compactness (examples, sequential compactness for metric
spaces).
Chapter 3, Section 1 (beginning). |
18.3.2024 |
Compactness (examples). Ultrafilters.
Chapter 3, Section 1 (with added example). |
22.3.2024 |
Compactness (ultrafilters criterion). Connectedness
(definition, examples).
Chapter 3, Section 1. Chapter 3, Section 2 (beginning). |
25.3.2024 |
Connectedness (examples, connected components).
Chapter 3, Section 2 (beginning). |
8.4.2024 |
Completeness (survey and examples).
Chapter 3, Section 3. |
12.4.2024 |
Local compactness and connectedness: definition,
examples, basic properties.
Chapter 3, Section 3. Chapter IV The product topology: definition, continuity properties. Chapter 4, Section 1. |
15.4.2024 |
The product topology. Tychonov's Theorem.
Chapter 4, Section 1. |
19.4.2024 |
Proof of Tychonov's Theorem. The quotient topology,
definition and examples.
Chapter 4, Section 1, Chapter 4, Section 2 (updated). |
22.4.2024 |
Functions: normal spaces, Urysohn's Theorem, examples.
Chapter 4, Section 3. |
26.4.2024 |
Proof of Urysohn's Theorem. Ascoli's Theorem and the
Stone-Weierstrass Theorem.
Chapter 4, Section 3. |
29.4.2024 |
Chapter V
Motivation for algebraic topology. Definition of homotopy and contractibility. Examples; the circle is not contractible. Chapter 5, Section 1 (beginning). |
3.5.2024 |
Paths and loops; path-connected spaces. Definition of
the fundamental group(oid).
Chapter 5, Section 1. |
6.5.2024 |
Some examples and properties of the fundamental group.
Chapter 5, Section 2 (beginning). |
10.5.2024 |
"Functoriality" of the fundamental group; applications.
Chapter 5, Section 2. Chapter VI Covering theory: definition of covering spaces, examples. Chapter 6 (beginning). |
13.5.2024 |
Covering theory: examples of quotient by a discrete
group.
Chapter 6 (beginning). |
17.5.2024 |
The homotopy lifting property and application to the
computation of fundamental groups.
Chapter 6 (beginning). |
24.5.2024 |
Proof of the homotopy lifting property. Definition and
existence of the universal covering space.
Chapter 6 (beginning). |
27.5.2024 |
Construction of the universal covering
space.
Chapter 6 (beginning). |
31.5.2024 |
Classification of covering spaces using the universal
cover.
Chapter 6. Chapter VI Final remarks and perspectives. Chapter 7. |
Time | Room | TA | Language |
---|---|---|---|
Mo 10-12 | CAB G 59 | Finn Michler | German |
Mo 10-12 | CHN D 48 | Adrian Spiess | German |
Mo 10-12 | HG E 33.1 | Dominique Garmier | English |
Mo 10-12 | ML F 40 | Maria Morariu | English |
Mo 10-12 | ML H 41.1 | Vincent Hoffmann | German |