Difference between revisions of "Topologie - 2019"

Revision as of 10:24, 13 August 2019

Andrea, 12.08.2019 10:50-11:10

Topics:

• What is the Fundamental group of the Möbius strip?

When two spaces have the same Fundamental Group? Def of Homotopy equivalent spaces and find the homotopy equivalence between the cirle and Mobius strip.

• exercise: you have (xn) sequence with limit x. Prove that the set containing only the sequence and the limit is compact.

I took a long time for the first part and unfortunately after there was no time left.

Sisto is calm and helps you if you make confusion.

Nico, 13.08.2019, 11:30-11:50

Questions:

• Let (\X\) be a compact metric space. Suppose that (\ f: X \rightarrow Y \) is continuous and (\ f(x) \neq x \) for all (\ x \in X \). Prove that there exists (\ \epsilon > 0 \) so that (\ d(x,f(x)) >\epsilon \) for all (\ x \in X \).
• Let (\ f , g : X \rightarrow Y \) be a map. Show how the induced map of (\ f \) and (\ g \) are related.

I needed more than half of the time for the first questions where I couldn't conclude at the end. He tried to help me and sometimes he let me think for a couple of seconds without saying something. We run out of time before I finished all for the second question.

In front of his office is a couch to wait with some chocolate one could eat, that is really nice.