Related papers: A note on free paratopological groups
Some boundedness properties of function spaces (considered as topological groups) are studied.
This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.
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 mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If $A$ and $B$ are $\omega$-narrow subsets of a paratopological group $G$, then $AB$ is…
As a common non-trivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassian group and initiate its comprehensive study. Specifically,…
This is a survey article on the currently very active research area of free (=non-commutative) real algebra and geometry. We first review some of the important results from the commutative theory, and then explain similarities and…
In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.
This paper is devoted to the study of a natural group topology on the fundamental group which remembers local properties of spaces forgotten by covering space theory and weak homotopy type. It is known that viewing the fundamental group as…
A finitely generated group G is termed parafree if it is residually nilpotent and it has the same isomorphism types of nilpotent quotients as some free group. The two main results of this MSc. Thesis characterise the parafreeness of two…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
In this paper, we study the class of free hyperplane arrangements. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over $\mathbb{Q}$.
The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…
Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are studied.
In this paper, we consider the relation between the group freeness and the amalgamated freeness of crossed product algebras.
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.
In this article, we study geometric properties of nilpotent groups. We find a geometric criterion for the word problem for the finitely generated free nilpotent groups. By geometric criterion, we mean a way to determine whether two words…
This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
This note provides an alternate account of Calegari's rationality theorem for stable commutator length in free groups.