Kanovei, Vladimir; Reeken, Michael A nonstandard proof of the Jordan curve theorem. (English) Zbl 0938.54041 Real Anal. Exch. 24(1998-99), No. 1, 161-169 (1999). Summary: We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is self-contained, except that the Jordan theorem for polygons is taken for granted. Cited in 1 Document MSC: 54J05 Nonstandard topology 03H05 Nonstandard models in mathematics Keywords:Jordan curve theorem; nonstandard analysis × Cite Format Result Cite Review PDF Full Text: arXiv