Éléments d'une théorie non standard des groupes topologiques
Embedding a topological group into a connected group
It was proved in [HM] that each topological group (G,·,τ) may be embedded into a connected topological group (Ĝ,•,τ̂). In fact, two methods of introducing τ̂ were given. In this note we show relations between them.
Embedding topological semigroups into the hyperspaces over topological groups
Enlarging the convergence on the real line via metrizable group topologies
Epics in the category of k-groups need not have dense range
Equivalence of certain free topological groups
In this paper we give a complete isomorphical classification of free topological groups of locally compact zero-dimensional separable metric spaces . From this classification we obtain for locally compact zero-dimensional separable metric spaces and that the free topological groups and are isomorphic if and only if and are linearly homeomorphic.
Equivariant completions
An important consequence of a result of Katětov and Morita states that every metrizable space is contained in a complete metrizable space of the same dimension. We give an equivariant version of this fact in the case of a locally compact -compact acting group.
Errata-Corrige. Une rectification dans notre travail «Sur les produits filtrés de certains groupes topologiques»
Every reasonably sized matrix group is a subgroup of S ∞
Every reasonably sized matrix group has an injective homomorphism into the group of all bijections of the natural numbers. However, not every reasonably sized simple group has an injective homomorphism into .
Example of a convergence commutative group which is not separated
Extendibility, monodromy, and local triviality for topological groupoids.
Extension properties of WS-groups.
Extensions of Pontryagin Duality.
Extensions of topological and semitopological groups and the product operation
The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group that is not Dieudonné complete one can find a Dieudonné complete group such that the Dieudonné completion of is not a topological group containing as a subgroup. Using Korovin’s construction of -dense orbits, we present some examples showing that some results on topological groups are not valid for semitopological...
Extremal phenomena in certain classes of totally bounded groups [Book]
Extremal pseudocompact Abelian groups: A unified treatment
The authors have shown [Proc. Amer. Math. Soc. 135 (2007), 4039--4044] that every nonmetrizable, pseudocompact abelian group has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology. Here they give a comprehensive, direct and self-contained proof of this result.