Related papers: Approximation of structures:local and global
We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…
We present a selection of results contributing to a structure theory of totally disconnected locally compact groups.
We prove continuity results for abstract epimorphisms of locally compact groups onto finitely generated groups.
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…
The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
We introduce a framework of structural approximation to represent Lorentz-invariant Minkowski space-time as the limit of finite cyclic lattices, each equipped with the action of a finite quasi-Lorentz group. This construction provides a…
We establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we…
Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that all of them can be exponentiated to cocycle matched pairs of…
We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…
Let X be an affine variety and L be a solvable Lie subalgebra of Lie(Aut(X)) generated by a finite collection of locally finite Lie subalgebras. The authors of [arXiv:2507.09679] wondered whether L is itself locally finite. Here we present…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to…
We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…
We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive…
We define a class of groups equipped with an invariant probability measure, which includes all compact groups and is closed under taking ultraproducts with the induced Loeb measure; in fact, this class also contains the ultraproducts all…