Related papers: A short proof of Cramer's theorem in R
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.
A very simple but useful almost sure convergence theorem of probability is given.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We give a short proof of the Buchstaber-Rees theorem concerning symmetric powers. The proof is based on the notion of a formal characteristic function of a linear map of algebras.
We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple…
We describe two distinct simple, short and self contained proofs of the composition lemma.
We record an explicit proof of the theorem that lifts a two-variable adjunction to the arrow categories of its domains.
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
We give a short proof of Ahlfors' theorem on covering surfaces.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
In this paper we prove the Jordan-Kronecker theorem which gives a canonical form for a pair of skew-symmetric bilinear forms on a finite-dimensional vector space over an algebraically closed field.
Cramer's rules for some left, right and two-sided quaternion matrix equations are obtained within the framework of the theory of the column and row determinants.
In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any…
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…
A short proof of the elliptical range theorem concerning the numerical range of $2\times2$ complex matrices is given.
We give a geometric proof of the Routh's theorem for tetrahedra.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.