Related papers: On topological rough groups

Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…

As a branch of algebraic and differential topology of manifolds, the theory of Morse functions and their higher dimensional versions or fold maps and its application to algebraic and differential topology of manifolds is fundamental,…

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…

This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…

In this paper, we introduce round and sleek topological spaces and study their properties.

The work starts a series of papers on topological radicals and their applications. Among other results we present a theory of radicals related to the joint tensor radius.

In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate categories, based on the details of the continuity required of the group multiplication. We define $\NP_1$- and…

This paper surveys some results and methods in topological transformation groups.

We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…

Quantum groups have been studied within several areas of mathematics and mathematical physics. This has led to different approaches, each of them with their own techniques and conventions. Starting with Hopf algebras, where there is a…

Given a $T$-rough definably amenable $T$-rough approximate subgroup $A$ of a group in some first-order structure, there is a type-definable subgroup $H$ normalised by $A$ and contained in $A^4$ of bounded index in $\langle A\rangle$.

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.

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 classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.

We study topological groups of monotonic autohomeomorphisms on a generalized ordered space $L$. We find a condition that is necessary and sufficient for the set of all monotonic autohomeomorphisms on $L$ along with the function composition…

We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.