Topologie I, Sommersemester 2017

Previous announcements (no longer relevant)

• 2.10.2017: For people preparing for the upcoming exam (second attempt), I will hold extra office hours on Friday, 6.10.2017 from 13:00 to 15:00 in 1.301.
• 20.07.2017: There will be extra office hours on Monday, 24.07.2017 from 15:00 to 17:00 in 1.301. This is especially for anyone who'd like to discuss the problems on the practice exam, but all questions are welcome.
• 18.07.2017: There is now a Practice exam / Probeklausur posted below. There will be no more problem sets.
• 17.07.2017: To avoid conflict with the Stochastik I Klausur on Wednesday, this week's Übung has been rescheduled for Thursday 15:00-17:00 (c.t.) in room 3.007 (RUD 25). The due date of Problem Set 11 is extended accordingly to Thursday (you may hand it in as usual in lecture or at the beginning of the Übung). For the benefit of anyone who cannot make the Thursday time, we will have extra office hours (Wendl: 1.301, Schmäschke 1.303) on Wednesday 11:00-13:00.
• 28.06.2017: The online teaching evaluation website is accepting your opinions from now until July 6. For anyone who doesn't already have the necessary password (token), I will give it out in lecture on June 29.
• 7.06.2017: The takehome midterm will be distributed next Wednesday (the 14th) and will be due two weeks later. There will be no regular problem sets for those two weeks.
• 10.06.2017: There was an important typo in the version of Problem Set 8 handed out in class. In Problem 1(h), it should refer to the "converse of part (g)", not "part (f)". The version below has been corrected.
• 7.06.2017: Problem Set 8 will be distributed on Thursday this week. It will appear on this page later today (Wednesday).
• 10.05.2017: A question at the end of today's Übung uncovered yet another small error in Problem Set 3 (the open cover in Problem 2(b) was not open), so the version posted below has been further corrected.
• 8.05.2017: Sorry, the end of last Thursday's lecture was a bit of a mess, so in addition to the error mentioned below, the definitions of local connectedness and local path-connectedness were stated incorrectly. Here are the correct definitions: a space is locally (path-)connected if for every point x in the space, every neighborhood of x contains a (path-)connected neighborhood of x. In other words, every point has a neighborhood base consisting of (path-)connected sets. Note that by this definition, a space may be (path-)connected (a global property, i.e. it is a property of the whole space rather than of every neighborhood in the space) even if it is not locally (path-)connected (a local property, i.e. it depends on every neighborhood). This is relevant to Problem 4 on this week's homework.
• 7.05.2017: There was also an error in the statement of Problem 3(b) on this week's problem set; it has been corrected in the version posted below.
• 4.05.2017: There was an important error on the board in today's lecture: a space X is connected if and only if it does not decompose into two disjoint nonempty open subsets. (What I failed to say in the lecture was that the two subsets must also cover X, i.e. their union is X --- otherwise one can think up trivial examples of spaces that obviously should be connected but aren't. The definition is indeed equivalent to saying that X has no open and closed subsets other than itself and the empty set; that part of what I said was correct.)
• 26.04.2017: Due to overcrowding, the location for the Übung has been changed to room 1.013 in Rudower Chaussee 25. (The course information sheets above have been edited to reflect this change.)
• 26.04.2017: Problem Set 2 is now officially available below.
• 26.04.2017: The new problem set will be distributed officially on Thursday this week instead of Wednesday, but an incomplete preliminary version is already available below.
• 12.04.2017: Die Übung findet in der ersten Semesterwoche nicht statt. / The problem class will not meet in the first week of the semester.