Related papers: A simple case within Nash-Moser-Ekeland theory

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

We provide a simple proof of Kamp's theorem.

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

We present in this work a new and simple proof of the false centre theorem.

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

A very short proof of Kneser's theorem via transversal is given.

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

A very simple but useful almost sure convergence theorem of probability is given.

In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.

We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

We give an elementary proof to Hasse theorem.

An technically interesting proof of a known theorem.