A subset A of a topological group G is said to be totally bounded if for any neighborhood U of
the identity there exists a finite subset K c G such that A~(KU N UK). If the subset G of a …

Let G be a locally compact totally disconnected topological group. If G contains a closed
subgroup A which is isomorphic with a discrete finitely generated free abelian group, such …

If G is an Abelian group, then G# is G with its maximal totally bounded group topology. We
prove that every A⊆ G# contains a closed (in G#) and discrete subset B such that| B|=| A …

A family $\Phi $ of continuous endomorphisms of a topological group $ G $ is said to be
small if for every subgroup $ H $ of $ G $ of cardinality ${\text {card}}(H)<{\text {card}}(G) …

For certain classes A of topological group topologies on a group G, we determine those
cardinals β which arise as the length of a chain in A. We show, for example, that if G is …

A topological group G will be said to have property U if every continuous real-valued
function/on G is uniformly continuous (ie for every e> 0 there is a neighborhood N of the …

We define a variety V, of topological groups to be a family of topological groups closed
under cartesian products, quotient groups and subgroups. The class of groups, which with …

It is shown that for each positive integer n, there exists a nondiscrete Hausdorff topological
group of cardinality ℵ n with no proper subgroup of the same cardinality and with each …

QUOTIENT GROUPS OF TOPOLOGICAL GROUPS WITH NO SMALL SUBGROUPS 625 Page
1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 31, No. 2, February …

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 …