Related papers: The Marker-Steinhorn Theorem

We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".

In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

We give a new proof of Lucas' Theorem in elementary number theory.

In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.

An technically interesting proof of a known theorem.

We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.

By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.

We give a complete self-contained proof of Statman's finite completeness theorem and of a corollary of this theorem stating that the $\lambda$-definability conjecture implies the higher-order matching conjecture.

We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.

We provide a simple proof of Kamp's theorem.

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

We prove the Aharoni Berger Conjecture

We give a counting based proof of the Graham Pollak Theorem

In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.