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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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Paul

Posts: 428
Registered: 7/12/10
Re: Problem understanding proof of Jordan Curve Theorem
Posted: Jul 9, 2013 5:56 PM
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On Tuesday, July 9, 2013 10:53:04 PM UTC+1, Paul wrote:
> I have been reading Tverberg's proof of the Jordan Curve Theorem:
>
> http://www.maths.ed.ac.uk/~aar/jordan/tverberg.pdf
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>
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> 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.
>
>
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> Thank you very much for your help,
>




To clarify, when I say that I can't justify "that assertion", I mean the assertion about disk D. I _don't_ mean the assertion that continuous functions on compact sets attain their suprema.

Paul Epstein



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