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Topic: Problem understanding proof of Jordan Curve Theorem
Replies: 13   Last Post: Jul 12, 2013 9:25 AM

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Registered: 7/12/10
Problem understanding proof of Jordan Curve Theorem
Posted: Jul 9, 2013 5:53 PM
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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,

Paul Epstein

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