Topology Spring 2024

Lecturer
Emmanuel Kowalski
Coordinator
Francesco Naccarato
Lectures (English)
Mondays, 9 to 10 in HG F.3
Fridays, 8 to 10 in HG G 5.
Exercise classes (English and German): Mondays, 10:00 to 12:00.
Semesterpräsenz: Wednesdays, 16.15 to 18 in HG E1.2
These are office hours for the students to ask questions about the lectures and exercises.

Content

Introduction to topology (foundations, examples, fundamental theorems and introduction to the fundamental group and covering theory).

Quizzes

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.

Exercises

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
Serie 10 Serie 10 (EN) May 8 Submission

Summary of the lectures

We indicate here the topics discussed in each lecture, with references to the literature where applicable, and with links to the lecture notes.
The video recordings of the lectures are available on the ETH Video portal.
DayContent
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).

Übungsgruppen

TimeRoomTALanguage
Mo 10-12CAB G 59Finn MichlerGerman
Mo 10-12CHN D 48Adrian SpiessGerman
Mo 10-12HG E 33.1Dominique GarmierEnglish
Mo 10-12ML F 40Maria MorariuEnglish
Mo 10-12ML H 41.1Vincent HoffmannGerman

Literature