FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES Page 1 Mathematics of the
USSR-Izvestiya FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES To cite this …

In this paper the free topological vector space V (X) over a Tychonoff space X is defined and
studied. It is proved that V (X) is ak ω-space if and only if X is ak ω-space. If X is infinite, then …

A maximally almost periodic topological (MAP) group G respects P if P (G)= P (G^+), where
G^+ is the group G endowed with the Bohr topology and P stands for the subsets of G that …

We give a complete description of the topological spaces X such that the free abelian
topological group A (X) embeds into the free abelian topological group A (I) on the closed …

Tk theory of free topological groups was initiated by Markov [I *1] and Graev [Sj in the early
1940s. Since that tim?, and parti Page 1 j The uaiforasr frcaf tiqologicalt group over 8 uniform …

It is shown that under mild conditions the path-component of the identity in the dual group $
G\hat\emptyset $ of an Abelian topological group G is precisely the union of the one …

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 …

The known explicit descriptions of the topology of free and free Abelian topological groups
are collected. Examples of the application of such descriptions by various authors to study …

We survey the present trends in theory of universal arrows to forgetful functors from various
categories of topological algebra and functional analysis to categories of topology and …

We discuss various generalisations of countable compactness for topological groups that
are related to completeness. The sequentially complete groups form a class closed with …