Related papers: Ramsey Theory on Generalized Baire Space

The well-known Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey: Given any Borel subset $\mathcal{X}\subseteq [\omega]^{\omega}$, where $[\omega]^{\omega}$ is endowed with the metric topology, each infinite…

An abstract version of Galvin's lemma is proven, within the framework of the theory of Ramsey spaces. Some instances of it are explored.

We develop Descriptive Set Theory in Generalized Baire Spaces without assuming $\kappa^{<\kappa}=\kappa$. We point out that without this assumption the basic topological concepts of these spaces have to be slightly modified in order to…

Topological Ramsey theory studies a class of combinatorial topological spaces, known as topological Ramsey spaces, unifying the essential features of those combinatorial frames where the Ramsey property is equivalent to the Baire property.…

We prove a Bakry-\'Emery generalization of a theorem of Petersen and Wilhelm, itself a generalization of a theorem of Frankel, that closed minimal hypersurfaces in a complete manifold with a suitable curvature bound must intersect. We then…

We study the Ramsey property for vector spaces over finite fields with bilinear forms. We prove that symplectic spaces over finite fields do not have the Ramsey property. We also describe vector spaces with skew symmetric bilinear forms and…

This paper classifies different fragments of the Galvin-Prikry theorem, an infinite dimensional generalization of Ramsey's theorem, in terms of their uniform computational content (Weihrauch degree). It can be seen as a continuation of…

We prove a generalization of Gowers' theorem for $\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\mathrm{FIN}_{k}\rightarrow \mathrm{FIN}_{k-1}$, one considers all maps from $\mathrm{FIN}_{k}$ to $\mathrm{FIN}_{j}$ for…

In this paper we prove that the Prym map, from the space of double coverings of a curve of genus g with r branch points to the moduli space of abelian varieties, is generically injective if r>6 and g>1, r=6 and g>2, r=4 and g>4, r=2 and…

We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.

In this paper we establish a generalization of Bombieri-Vinogradov theorem for primes represented by a fixed positive definite binary quadratic form. Then we apply this theorem to generalize a result of Vatwani on bounded gap between…

We consider generalizations of the drifted Laplacian and the Bakry-\'Emery-Ricci tensor, and we prove a version of the mean curvature comparison theorem. Consequently, we prove a Myers-type theorem and a generalization of the…

In this paper, we successfully set up a generalized sphere theorem for compact Riemannian manifolds with radial Ricci curvature bounded.

A general local center manifold theorem around stationary trajectories is proved for nonlinear cocycles acting on measurable fields of Banach spaces.

We proved a KAM theorem on existence of invariant tori in generalized Hamiltonian systems without action-angle variables. It is a generalization of the result of de la Llave et al. [Llave, 2005] that deals with canonical Hamiltonian system.

We prove a general Ramsey theorem for trees with a successor operation. This theorem is a common generalization of the Carlson-Simpson Theorem and the Milliken Tree Theorem for regularly branching trees. Our theorem has a number of…

In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…

We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor-Riesz bases and a constant curvature connection on projective modules over noncommutative tori.

We show how to recover a general hypersurface in $\mathbb{P}^n$ of sufficiently large degree $d$ dividing $n+1$, from its finite order variation of Hodge structure. We also analyze the two other series of cases not covered by Donagi's…

It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary…