Related papers: On local matching property in groups and vector sp…
If F is a type-definable family of commensurable subsets, subgroups or sub-vector spaces in a metric structure, then there is an invariant subset, subgroup or sub-vector space commensurable with F. This in particular applies to…
A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally…
We construct a framework which gives intuitive representation of local cohomology groups. By defining the concrete mappings among them, we show their equivalence. As an application, we justify intuitive representation of Laplace…
When studying the properties of a ring $R$, it is often useful to compare $R$ to other rings whose properties are already known. In this paper, we define three ways in which a subring $R$ might be compared to a larger ring $T$: being…
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…
We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…
The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
The article explores function terms within uniform theories. It examines the uniformity of these theories through an algebraic lens. The paper compares the uniformity of terms and predicates within axiom schemas. It demonstrates the…
We extend to semi-abelian categories the notion of characteristic subobject, which is widely used in group theory and in the theory of Lie algebras. Moreover, we show that many of the classical properties of characteristic subgroups of a…
We present elements of a theory of translation-invariant integration on finite dimensional vector spaces and on GL_n over a valuation field with local field as residue field. We then discuss the case of an arbitrary algebraic group. This…
We prove that the homotopy theory of parametrized spaces embeds fully and faithfully in the homotopy theory of simplicial presheaves, and that its essential image consists of the locally homotopically constant objects. This gives a…
We give a characterization of ramification groups of local fields with imperfect residue fields, using those for local fields with perfect residue fields. As an application, we reprove an equality of ramification groups for abelian…
We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…
In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups $\operatorname{GL}_{1}$ defined over $p$-adic fields $K$. We do this by redeveloping the theory of proalgebraic groups and use this…
Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…
In this paper, we define and study (co)homology theories of a compatible associative algebra $A$. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define…
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution,…