Related papers: On Fabry's Gap Theorem

A proof based on the Chern-Gauss-Bonnet Theorem is given to Hopf Theorem concerning the degree of the Gauss map of a hypersurface in $\mathbb{R}^n$.

In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We apply Vaaler's lemma and the Erd\H{o}s-Turan inequality to…

We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of a space B are replaced by a locally sectionable map to B.

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

We generalize Rothberger's theorem for regular lambda. We prove that the discrepancy between the pseudointersection number and the towering number is limited, under some reasobable assumption

There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new ZJ-type subgroups of a $p$-group $S$, that contain…

We generalize several classical theorems in extremal combinatorics by replacing a global constraint with an inequality which holds for all objects in a given class. In particular we obtain generalizations of Tur\'an's theorem, the…

We provide sufficient conditions for the existence of a global diffeomorphism between tame Fr\'{e}chet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredient in the proof of the main theorem.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We prove a linear recurrence relation for a large family of generalized Schreier sets, which generalizes the Fibonacci recurrence proved by Bird and higher order Fibonacci recurrence proved by the second author et al. Furthermore, we show a…

We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.

We prove a natural generalization of the classical three gap theorem, for rotations on adelic tori. Our proof is an adaptation to the adeles of the lattice based approach to gaps problems in Diophantine approximation originally introduced…

We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the…

We show that although the Galvin-Prikry Theorem does not hold on generalized Baire space with the standard topology, there are similar theorems which do hold on generalized Baire space with certain coarser topologies.

The Theorems of Pappus and Desargues are generalized by two special formulas that hold in the three-dimensional vector space over a field.

We prove a generalized Fej\'er's theorem for locally compact groups.