It is shown that a free topological group on a ${k_\omega} $-space is a ${k_\omega} $-
space. Using this it is proved that if $ X $ is a ${k_\omega} $-group then it is a quotient of a …

In this paper we investigate the topological structure of free topological universal algebras
with given continuous signature. We establish some properties of compact subsets of free …

We give a negative answer to the following question of Bel'nov: Can every Tychonoff space
X be imbedded as a subspace of a topological group G so that dim G⩽ dim X? We show that …

By a variety of topological algebras we mean a class V of topological algebras of a fixed type
closed under the formation of subalgebras, products and quotients (ie images under …

1. Varieties of groups. The study of varieties of groups (more generally, varieties of algebras)
has its roots in the work of Birkhoff [4] and Neumann [60] in the 1930's. A variety of groups …

In this note the notion of a free topological product Gα of a set {Gα} of topological groups is
introduced. It is shown that it always exists, is unique and is algebraically isomorphic to the …

Known and new results on free Boolean topological groups are collected. An account of the
properties that these groups share with free or free Abelian topological groups and …

AV Arkhangel'skiĭ asked in 1981 if the variety V of topological groups generated by free
topological groups on metrizable spaces coincides with the class of all topological groups …

In this note the Stone-Čech compactification is used to produce short proofs of two theorems
on the structure of free topological groups. The first is: The free topological group on any …

This paper continues the invèstigation of varieties of topological groups. It is shown that the
family of all varieties of topological groups with any given underlying algebraic variety is a …