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 > > > > 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, >
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.