Inhaltsbeschreibung / course description and syllabus

Moodle
(für Einschreibeschlüssel siehe Inhaltsbeschreibung oben / see course description above for the enrolment key)

Vorlesungsskript / lecture notes
Last update: 13.05.2026.
This is a complete set of lecture notes for the courses Topology I-III, the first portion of which will be updated occasionally as this course progresses.

Ankündigungen / Announcements

• 13.04.2026: Die Übung findet in der ersten Semesterwoche nicht statt. / There will be no problem session (Übung) in the first week of the semester.
• 20.04.2026: Starting from 21.04.2026 (the third lecture), the lectures for this course will take place in room 1.013 instead of room 1.115.
• 20.04.2026: The first (and only the first!) meeting of the problem session / Übung, on 22.04.2026, will take place in room 1.013.
• 20.04.2026: Starting from 29.04.2026 (the third week), the problem session / Übung will be divided into two sections meeting at the same time (Wednesdays 15:15-16:45) in separate rooms:
  • Group 1 (J. Campos): room 1.011
  • Group 2 (S. Kumar): room 3.006
  A tool is available on the moodle for students to select which section they attend.
• 11.05.2026: As of Problem Set 5, it is possible to submit solutions and receive grades for select problems on the problem sets. See the syllabus linked above for more on the incentive for doing this.

Übungsblätter / Problem sets

Weekly problem sets (consisting of exercises contained in the lecture notes) will be posted here by Wednesday of each week and discussed in the Übung on the following Wednesday. The exercises marked with an asterisk(*) should be considered essential, but it is highly recommended that you at least think through all exercises as a form of mental preparation for the following week's lectures.

New (11.05.2026): From Problem Set 5 onward, it is possible to submit solutions to the problems labelled with the symbol (†) and receive grades for them. Solutions can be uploaded to the moodle until exactly 15:15 on Wednesday, i.e. the beginning of the Übung.

Important: Press the reload button on the lecture notes to make sure you have the most recent version before looking for the week's exercises; their numbers will change, so you are unlikely to find them if you do not do this!

• Problem Set 1 (to be discussed 22.04.2026): Exercises 2.3, 2.4 (especially parts (a)(*) and (d)(*)), 2.5 (especially part (c)(*)), 2.6(*) and 2.7
• Problem Set 2 (to be discussed 29.04.2026): Exercises 3.3, 3.4 (especially part (c)(*)), 3.5, 3.6, 4.1(*), 4.2 (especially part (b)(*)), 4.3 and 4.4(*)
• Problem Set 3 (to be discussed 6.05.2026): Exercises 5.2 (especially part (b)(*)), 5.3 (especially part (a)(*)), 5.4, 6.2 (especially part (d)(*)), 6.3, 6.4 (especially part (c)(*)) and 6.5 (especially part (b)(*))
• Problem Set 4 (to be discussed 13.05.2026): Exercises 7.3, 7.4, 7.5, 7.6(*), 7.7 (especially part (a)(*)), 7.8 (especially part (b)(*)), 7.9 (especially parts (d)(*) and (e)(*))
• Problem Set 5 (due 19.05.2026): Exercises 8.2, 9.1 (especially part (b)(†)), 10.3 (especially part (c)(†)), 10.5 (especially parts (b)(†), (d)(†) and (e)(†)), 10.6