Real Analysis Exchange

A Nonstandard Proof of the Jordan Curve Theorem

Vladimir Kanovei and Michael Reeken

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Abstract

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

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

Dates
First available in Project Euclid: 23 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.rae/1300906020

Mathematical Reviews number (MathSciNet)
MR1691743

Zentralblatt MATH identifier
0938.54041

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

Keywords
Jordan curve theorem nonstandard analysis

Citation

Kanovei, Vladimir; Reeken, Michael. A Nonstandard Proof of the Jordan Curve Theorem. Real Anal. Exchange 24 (1998), no. 1, 161--170. https://projecteuclid.org/euclid.rae/1300906020


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