Related papers: A short and elegant proof of a theorem of J.-E. Pi…
This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
We give a new simpler proof of a theorem of Jayne and Rogers.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
In this note we give a detailed proof of a theorem of Aubin.
Here, we give a self-contained and elementary proof of a minimax theorem due to Fan in a simplified setting that can be taught in an advanced undergraduate course. Our proof follows Nikaido's argument with some simplifications.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
A very short proof of Kneser's theorem via transversal is given.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
In this article, we give another visual proof of $\pi^e < e^\pi$.
The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
We present a short and self-contained proof of the choosability version of Brooks' theorem.
Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather…