Related papers: A-sets

Geometry of buildings is used to prove some homological properties of the category of smooth representations of a reductive p-adic group (Kazhdan's "pairing conjecture", Bernstein's description of homological duality in terms of…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

We give a simple characterization of all perfectoid profinite \'{e}tale covers of abelian varieties in terms of the Hodge-Tate filtration on the $p$-adic Tate module. We also compute the geometric Sen morphism for all profinite $p$-adic Lie…

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we…

In this paper we show that certain generalizations of the $C^r$-Whitney topology, which include the H\"older-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the Baire property, to wit, the countable intersection of open…

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study…

Let $F$ be a totally real field in which $p$ is unramified. We prove that, if a cuspidal overconvergent Hilbert cuspidal form has small slopes under $U_p$-operators, then it is classical. Our method follows the original cohomological…

We show that even for subsets X of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Gamma,Gamma), asserting that for each countable family of open gamma-covers of X, there is a choice…

We introduce a class of proper posets which is preserved under countable support iterations, includes $\omega^\omega$-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the…

We study the ideal of meager sets and related ideals.

The fundamental groupoid of a space becomes enriched over the category of topological spaces when the hom-sets are endowed with topologies intimately related to universal constructions of topological groups. This paper is devoted to a…

Which Isbell--Mr\'owka spaces ($\Psi$-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a…

Iwasa investigated the preservation of various covering properties of opological spaces under Cohen forcing. By improving the argument in Iwasa's paper, we prove that the Rothberger property, the Menger property and selective screenability…

We present and study the concept of $m$-periodic Gorenstein objects relative to a pair $(\mathcal{A,B})$ of classes of objects in an abelian category, as a generalization of $m$-strongly Gorenstein projective modules over associative rings.…

The product of a Sierpinski set and a Lusin set has Menger's property. The product of a gamma set and a Lusin set has Rothberger's property.

We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we…

Let $G$ and $H$ be locally compact, second countable groups. Assume that $G$ acts in a measure class preserving way on a standard probability space $(X,\mu)$ such that $L^\infty(X,\mu)$ has an invariant mean and that there is a Borel…

Morrey spaces can complement the boundedness properties of operators that Lebesgue spaces can not handle. Morrey spaces which we have been handling are called classical Morrey spaces. However, classical Morrey spaces are not totally enough…

We revisit a classical paper by Piatetski-Shapiro and Shafarevich on algebraic approach to uniformization and provide a partial solution of the problem, namely, whether the existence of proalgebraic quasi-homogeneous coverings of general…