Add to ORKGIn this paper we introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topo- logical vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over a hemicompact k{space are Schwartz groups. We also prove that every hemicompact k{space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group
AbstractWe define free groups in certain classes of abelian topological groups. Of special interest ...
AbstractIt is natural to extend the Grothendieck theorem on completeness, valid for locally convex t...
AbstractThe notion of locally quasi-convex abelian group, introduced by Vilenkin, is extended to max...
AbstractIn Außenhofer (2007) [4] it was shown that every kω group is a Schwartz group, a generalizat...
AbstractIt is proved that a locally quasi-convex group is a Schwartz group if and only if every cont...
Quasinormable spaces were introduced by Grothendieck [34] as a collection of spaces, with good stabi...
AbstractIn Außenhofer (2007) [4] it was shown that every kω group is a Schwartz group, a generalizat...
The present paper is a contribution to fill in a gap existing between the theory of topological vect...
AbstractIt is proved that a locally quasi-convex group is a Schwartz group if and only if every cont...
AbstractWe prove in this paper that for a Hausdorff group topology on an Abelian group with sufficie...
We give a complete description of the topological spaces X such that the free abelian topological gr...
We prove that the additive group (E*, τ k (E)) of an -Banach space E, with the topology τ k (E) of ...
AbstractFréchet–Urysohn (briefly F-U) property for topological spaces is known to be highly non-mult...
AbstractGiven a Tychonoff space X and classes U and V of topological groups, we say that a topologic...
It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topologi...
AbstractWe define free groups in certain classes of abelian topological groups. Of special interest ...
AbstractIt is natural to extend the Grothendieck theorem on completeness, valid for locally convex t...
AbstractThe notion of locally quasi-convex abelian group, introduced by Vilenkin, is extended to max...
AbstractIn Außenhofer (2007) [4] it was shown that every kω group is a Schwartz group, a generalizat...
AbstractIt is proved that a locally quasi-convex group is a Schwartz group if and only if every cont...
Quasinormable spaces were introduced by Grothendieck [34] as a collection of spaces, with good stabi...
AbstractIn Außenhofer (2007) [4] it was shown that every kω group is a Schwartz group, a generalizat...
The present paper is a contribution to fill in a gap existing between the theory of topological vect...
AbstractIt is proved that a locally quasi-convex group is a Schwartz group if and only if every cont...
AbstractWe prove in this paper that for a Hausdorff group topology on an Abelian group with sufficie...
We give a complete description of the topological spaces X such that the free abelian topological gr...
We prove that the additive group (E*, τ k (E)) of an -Banach space E, with the topology τ k (E) of ...
AbstractFréchet–Urysohn (briefly F-U) property for topological spaces is known to be highly non-mult...
AbstractGiven a Tychonoff space X and classes U and V of topological groups, we say that a topologic...
It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topologi...
AbstractWe define free groups in certain classes of abelian topological groups. Of special interest ...
AbstractIt is natural to extend the Grothendieck theorem on completeness, valid for locally convex t...
AbstractThe notion of locally quasi-convex abelian group, introduced by Vilenkin, is extended to max...