Date: Jul 9, 2013 5:53 PM
Subject: Problem understanding proof of Jordan Curve Theorem
I have been reading Tverberg's proof of the Jordan Curve Theorem:
I understand completely the proofs of lemmas 1 and 2, but I'm having trouble following the proof of lemma 3. In particular, it's not clear to me why there is a disc D with abs(a - b) maximal. This is probably a consequence of the fact that continuous functions on compact sets attain their maxima, but I can't justify that assertion.
Thank you very much for your help,