Topologie I - topologie générale
MATH-220
Introduction
Bienvenue au cours Topologie I !
Enseignante : Professeure Kathryn Hess Bellwad
Assistants : Daniel Cherpit, Joe Griggs, Bjørnar Hem, Vittorio Sandri, Dév Vorburger
Cours : le lundi de 13h15 à 15h, salle CE 4
Exercices : le lundi de 15h15 à 17h, salles MA 30 et MA 31
Séance RAQ : le vendredi 16 janvier de 14h à 16h, salle CE 1 103
- Announcements (Forum)
- Répartition par salle pour l'examen (File)
- Plan de salle: SG 1138 (File)
- Plan de salle: SG 0211 (File)
- Examen à blanc (File)
- Corrigé de l'examen à blanc (File)
- Introduction au cours (File)
- Plan du cours_v3 (File)
- Notes de cours de Luca Dalmas (File)
- The Lean Topology Game (URL)
- La chaîne Mediaspace du cours (URL)
- Notes de cours de Naoki Bourquenoud_v2 (File)
- Errata des notes de cours de N. Bourquenoud(v1) (File)
Semaine 1 : Espaces métriques
Semaine 2 : Espaces métriques
Semaine 3 : Jeûne fédéral (aucun cours)
Semaine 4 : L'axiomatique de la topologie
Semaine 5 : L'axiomatique de la topologie
Semaine 6 : L'axiomatique de la topologie
Semaine de pause!
Semaine 7 : L'axiomatique de la topologie
Semaine 8 : L'axiomatique de la topologie
Semaine 9 : L'axiomatique de la topologie
ATTENTION: Le cours a lieu cette semaine de 12h15 à 13h et de 14h15 à 15h
Semaine 10 : L'axiomatique de la topologie/Notions de séparabilité
- L'axiomatique de la topologie VII/Notions de séparabilité I (File)
- Série 9 (File)
- Corrigé 9 (File)
- Lean questionnaire (Questionnaire)
Semaine 11 : Notions de séparabilité
Semaine 12 : Notions de séparabilité
Semaine 13 : Autour de la notion de connexe
Semaine 14 : Autour de la notion de connexe
I'll be on ZOOM at 11h40 to take your questions.
This week, we will start a new chapter on metric spaces.
I will also prepare a quiz on chapters 2 and 3.
PS! I believe you can again give feedback through the IS-academia, please do so independently whether you like or don't like the course - it is helpful to have your feedback in any case.
We are continuing our study of metric spaces and see how the notion of compactness behaves in this setting - they behave very nicely!
We will also introduce the notion of completeness - this is a notion that only works for metric spaces.
I propose we meet a bit earlier, around 11h20 on ZOOM to also discuss your FEEDBACK (thanks to everyone who bothered to answer!) and the EXAMS.
We will first finish linking together compactness and completeness: we prove a metric space is compact, if it is totally bounded and and complete.
Thereafter we start working with the set of continuous functions from a metric space to a metric space. This will be an occasion for us to see how everything we have learned about compactness, completeness etc
will help us prove quite deep theorems, like Arzela-Ascoli theorem that you have used in complex analysis.
We will meet at 11h30 on ZOOM to quickly go through the QUIZ and then discuss the questions you might have.
Part of the videos are up, part will come quite a bit later today, because I just realized that the longest videos I recorded did in fact not record for technical reasons...so I have to redo them. Apologies! :)
We will prove Arzela-Ascoli theorem and look at how to talk about generic properties in topological spaces.
We meet at 11h40 in ZOOM for a Q&A session.
The videos will be there only very late, unfortunately - apologies.
The final week of the course. Basically the material is the Baire Category theorem, but you might have already looked into it.
I have prepared some materials for revision, and a mini-mock-exam.
I propose we meet at 11h15 on ZOOM to discuss the exam, the mock-exam and the revision.