Difference between revisions of "Topologie - 2018"

Revision as of 12:20, 27 August 2018

Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like me kicking you with my fists.

Tomás, 24.08.2018 11:30-11:50

Topics:

• First countable compact implies sequentially compact
• Exercise: For family \(C_i\) of connected sets, \(C_i \cap C_{i+1} \neq \emptyset\), show connected.

Sisto was super nice and friendly, yet it took me a long time to solve the exercise, and the time was over before we could do anything else. Wish I could have done much more.

Michael, 27.08.2018 11:30-11:50

Topics:

• First X,Y first countable, f continiuos (def open set) iff every sequence (xn) with limit x, f(xn) converges to f(x)
• f:X->X,f(x)=/x for all x in X, continuos, metric space, X comp., -> Exists Epsilon>0 s.t d(f(x),x)>=Epsiolon.

Sisto has a list with statements and exercises and chooses randomly.

Kaye, 27.08.2018 11:10-11:30

Topics:

• exercise: you have (xn) sequence with limit x. Prove that the set containing (I think he meant only, because the solution wouldn’t make sense, but he didn’t really say it.) the sequence and the limit is compact.
• f:R—>R continuous function in R. Proof of one direction of the equivalence between the definition of continuity with open sets and the epsilon, delta definition from analysis.
• the fundamental group: what is the “meaning” of x0? He wanted to know that if there exists a path gamma from x0 to y0, then we can find a group isomorphism between the two fundamental groups. (Proposition seen in class).

Then the time was already over! Sisto is really nice, and gives you time to think about the answer and gives useful hints if necessary.

Emanuel, 27.08 13:10-13:30

Topics:

• Prove that compact sets in Hausdorff spaces are closed.

• XxY, Y cpt, p:XxY -> X projection map, prove that p is a closed map. This was actually rather hard, but he was nice enough to say that beforehand. He had to help me a lot but we managed to do it in the end.

The atmosphere is super relaxed. He has a nice couch infront of his room and gives you chocolates :D

Skander, 27.08 13:50-14:10

Topics:

• Let X be a Hausdorff space, C a compact subset of X, show that C is closed.

• Exercise: For family \(C_i\) of connected sets, \(C_i \cap C_{i+1} \neq \emptyset\), show that the union of the connected sets is connected. (The luck for this one is absolutely unreal, I know)

Schöne Ferien euch allen! ;)))