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 MathSciNet
Nonstandard proof of Jordan Curve Theorem:
1) we approximate the curve with a hyper-polygon,
2) it happens to be possible to cut all loops of the polygon so that
the resulting simple polygon still approximates the curve 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.
See also
Fermat
Leibniz
Euler
Cauchy
Riemann
Cantor
Skolem
Heyting
Robinson
Nelson
Hrbacek
Infinitesimal topics
More on infinitesimals
Return to homepage