I need a short proff of the Jordan curve theorem please.
The one I have is 16 pages long and is for a little expo, so I need one a little shorter.
Thanks
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asked Mar 19, 2019 at 17:55
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1$\begingroup$ See J. Dieudonne, Foundations of modern analysis. AP. -New York & London. 1960, Appendix to Ch.9 to this end. It takes approximately 5 p. $\endgroup$– user64494Commented Mar 19, 2019 at 18:08
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1$\begingroup$ This proof takes about 2 pages, not including the proof of Brouwer’s fixed-point theorem: math.auckland.ac.nz/class750/section5.pdf . Actually, it comes from doi.org/10.1080/00029890.1984.11971517 . $\endgroup$– Emil JeřábekCommented Mar 19, 2019 at 18:13
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$\begingroup$ The proof from the Dieudonne's book is all-sufficient. $\endgroup$– user64494Commented Mar 19, 2019 at 18:17
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1$\begingroup$ If it's for exposition, consider proving it just for pl curves. The general proof covers non-rectifiable curves, so by conservation of difficulty it's either going to involve heavy machinery like Brouwer or it's going to be long and involved. $\endgroup$– NealCommented Mar 19, 2019 at 20:37
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