We exhibit natural classes of Polish topological groups $ G $ such that every continuous
action of $ G $ on a compact space has a fixed point, and observe that every group with this …

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 …

This paper initiates the formal study of those classes of locally convex spaces which are
closed under the taking of arbitrary subspaces, separated quotients, cartesian products and …

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 …

For a completely regular space X we denote by $ F (X) $ and $ A (X) $ the free topological
group of X and the free Abelian topological group of X, respectively, in the sense of Markov …