A Nonstandard Proof of the Jordan Curve Theorem
نویسندگان
چکیده
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 selfcontained, except for the Jordan theorem for polygons taken for granted.
منابع مشابه
A Nonstandard Proof of the Jordan Curve Theorem
In this paper a proof of the Jordan curve theorem will be presented. Some familiarity with the basic notions of nonstandard analysis is assumed. The rest of the paper is selfcontained except for some standard theorems about polygons. The theorem will be proved in what ought to be a natural way: by approximation by polygons. This method is not usually found in the standard proofs since the appro...
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