Talk:Knaster–Kuratowski–Mazurkiewicz lemma

Helping me understand a bit this theorem.
So I read Core (game theory) and have a physical hardcopy of D.B. Gillies' paper "Discriminatory and bargaining solutions to a class of symmetric n-person games." However this piece of math seems a bit new to me. I've taken several math courses such as Differentiable Manifolds, Martingales, Fourier Analysis, Algebra... so I may or may not have the right background to understand this work.

1: The motivation for this proof? Would it be true that this proof is novel due to it not being proven that the core is nonempty? Is it considering the general scenario of there exist situations where the core is nonempty?

2: It seems we have to go pretty far into math in order to show this, I mean an implication of this result is Brouwer's fixed-point theorem so it seems quite fundamental.

3: Following from Sperner's lemma is an interesting connection, combining both combinatorics and topology. I don't know this area very well so happy to hear other's thoughts on it. Theheezy (talk) 07:50, 7 July 2023 (UTC)