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.
"A Nonstandard Proof of the Jordan Curve Theorem." Real Anal. Exchange 24 (1) 161 - 170, 1998/1999.