This work contains a number of theorems about pseudocompact groups. Our first and most
useful theorem allows us to decide whether or not a given (totally bounded) group is …

For various pairs of topological properties such that P⇒ Q, we consider two questions:(A)
Does every topological group topology with P extend properly to a topological group …

Let A be a Banach algebra with a bounded left approximate identity. We denote,
respectively, by wap (A) and AA∗ the subspaces of A∗ consisting of the weakly almost …

The first main result formalizes the general principle that each totally bounded group G is
dense in some group H, not much larger than G, in which every subset of small cardinality …

Throughout this synopsis all topologies are Hausdorff topological group topologies, and⟨ G,
𝒯⟩ is assumed compact. The symbol w denotes weight. Definition. A subgroup H of⟨ G, 𝒯⟩ …

In this article we continue the study of R-factorizability in paratopological groups. It is shown
that:(1) all concepts of R-factorizability in paratopological groups coincide;(2) a Tychonoff …

Let $\mathcal {M} $ be the set of all probability measures on $\beta N $. Let G be a locally
compact, noncompact, amenable group. Then there is a one-one affine mapping of …

It is known that if P is either the property ω-bounded or countably compact, then for every
cardinal α⩾ ω there is a P-group G such that wG= α and no proper, dense subgroup of G is a …

A topological group is said to be locally pseudocompact if the identity has a pseudocompact
neighborhood (equivalently: if the identity has a local basis of pseudocompact …

After Bourbaki, a paratopological group is a group G with a topology such that the
multiplication map m: G x GG is continuous. For an infinite cardinal a, a paratopological …