Related papers: Constructive proof of the Carpenter's Theorem
This is the third installment in a series of papers on the subject of derived contact structures. In this paper, we formally introduce the notion of a Legendrian structure in the derived context and provide natural constructions. We then…
The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. It is shown that if the term "constructible theory" is defined in a way which satisfies certain…
A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of…
We consider the class of compact countable subsets of the real numbers $\mathbb{R}$. By using an appropriate partition, up to homeomorphism, of this class we give a detailed proof of a result shown by S. Mazurkiewicz and W. Sierpinski…
In a recent paper, G. Cz\'edli and E.\,T. Schmidt present a structure theorem for planar semimodular lattices. In this note, we present an alternative proof.
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
We give a short proof of Ahlfors' theorem on covering surfaces.
We prove combinatorial theorems concerning the stick principle and cardinal characteristics.
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…
It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
We present some new sharp constructions for the Szemer\'{e}di-Trotter theorem. These constructions generalize previous work of Erd\H{o}s, Elekes, Sheffer and Silier, Guth and Silier, and the author. In the past, arguments showing the…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
We show that the Jacobian conjecture of the two dimensional case is true.
We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).
Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions…
Beloved Curry--Howard correspondence tells that types are intuitionistic propositions, and in constructive math, a proof of proposition can be seen as some kind of a construction, or witness, conveying the information of the proposition. We…