Vladimir Kanovei

Vladimir Kanovei (1951-) is a mathematician based in Moscow, and co-author (with Michael Reeken) of a standard reference on axiomatic nonstandard analysis: Nonstandard Analysis, Axiomatically (Springer, 2004) https://link.springer.com/book/10.1007/978-3-662-08998-9

Vladimir Kanovei at Scholar

Vladimir Kanovei at MathSciNet

Nonstandard proof of Jordan Curve Theorem:
1) we approximate the curve by a hyper-polygon,
2) it turns out to be possible to cut all loops of the polygon so that the resulting simple polygon still approximates the curve in essentially the same way - this is the point where nonstandard arguments are clearer than classical;
3) we apply the polygonal JST, taking care that the partition of the hyperplane defined by the polygon induces the partition of the standard plane by the given curve, and derive required properties of the latter from the corresponding properties of the former taken for granted.