相关论文: A detailed proof of a theorem of Aubin

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).

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

Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…

In this paper we show an index theorem for gerbes

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

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

In this note we give the answer to the question posed by V. N. Dubinin concerning covering properties of complex polynomials

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

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

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.

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

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

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

An technically interesting proof of a known theorem.

In this note, we will give a short proof of an identity for cubic partitions.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

In this note, we derive a Leibniz rule for difference quotient.

We give a presentation of abelian class field theory.

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.