Real Analysis Exchange

A Nonstandard Proof of the Jordan Curve Theorem

Vladimir Kanovei and Michael Reeken

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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.

Article information

Real Anal. Exchange, Volume 24, Number 1 (1998), 161-170.

First available in Project Euclid: 23 March 2011

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Zentralblatt MATH identifier

Primary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 54J05: Nonstandard topology [See also 03H05]

Jordan curve theorem nonstandard analysis


Kanovei, Vladimir; Reeken, Michael. A Nonstandard Proof of the Jordan Curve Theorem. Real Anal. Exchange 24 (1998), no. 1, 161--170.

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