In this paper we study topological properties of topological groups and, first of all, cardinal
invariants of topological groups. Many of the relevant questions are subsumed under the …

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 …

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 …

In this paper we investigate the topological structure of the Graev free topological group over
the rationals. We show that this free group fails to be a k-space and fails to carry the weak …

A subset S of a topological group G is said to be a suitable set if (a) it has the discrete
topology,(b) it is a closed subset of G {1}, and (c) the subgroup generated by S is dense in …

We study compact, countably compact, pseudocompact, and functionally bounded sets in
extensions of topological groups. A property P is said to be a three space property if, for …

We prove that if X is a Tychonoff topological space, Y a subspace of X, and every bounded
continuous pseudometric on Y can be extended to a continuous pseudometric on X, then the …

In this paper, we study the topological structure of a universal construction related to
quasitopological groups: the free quasitopological group F q (X) on a space X. We show that …

The result often known as Joiner's lemma is fundamental in understanding the topology of
the free topological group F (X) on a Tychonoff space X. In this paper, an analogue of …

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 …