Related papers: Open mappings of locally compact groups

In this paper we introduce an open-closed cobordism category with maps to a background space. We identify the classifying space of this category for certain classes of background space. The key ingredient is the homology stability of…

Elements of the free group define interesting maps, known as word maps, on groups. It was previously observed by Lubotzky that every subset of a finite simple group that is closed under endomorphisms occurs as the image of some word map. We…

We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473

We present a selection of results contributing to a structure theory of totally disconnected locally compact groups.

Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…

We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…

This is a selection of open problems dealing with ``large'' (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of…

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

We establish a straightforward estimate for the number of open sets with fundamental group constraints needed to cover the total space of fibrations. This leads to vanishing results for simplicial volume and minimal volume entropy, e.g.,…

If an open subgroup of the group of the invertible measures on a LCA group is isometric to another, then the correspoinding underlying LCA groups are topologically isomorphic to each other.

We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…

In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can…

The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.

This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

In this paper we characterize the group of affine transformations of a flat affine simply connected manifold whose developing map is a diffeomorphism. This is proved by making use of some simple facts about homeomorphisms of $\mathbb{R}^n$…