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We prove that every dense subgroup of a topological abelian group has the same ‘convergence dual’ as the whole group. By the ‘convergence dual’ we mean the character group endowed with the continuous convergence structure. We draw as a corollary[...]texto impreso
A convergence structure ? on a set G is a set of pairs (F,x) consisting of a filter F on X and an element x?X satisfying a few simple axioms expressing the idea that F converges to x. A set with a convergence structure is a convergence space. It[...]texto impreso
Feechet-Urysohn (briefly F-U) property for topological spaces is known to be highly non-multiplicative: for instance, the square of a compact F-U space is not in general Frechet-Urysohn [P. Simon, A compact Frechet space whose square is not Frec[...]texto impreso
Bruguera Padró, M. Montserrat ; Chasco, M.J. ; Martín Peinador, Elena ; Tarieladze, Vaja | Elsevier Science | 2000-04-16It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, i[...]texto impreso
Martín Peinador, Elena ; Chasco, M.J. ; Tarieladze, Vaja | Polish Acad Sciencies Inst Mathematics | 1999The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is n[...]texto impreso
Let Gˆ denote the Pontryagin dual of an abelian topological group G. Then G is reflexive if it is topologically isomorphic to Gˆˆ, strongly reflexive if every closed subgroup and every Hausdorff quotient of G and of Gˆ is reflexive. It is well k[...]texto impreso
For an abelian topological group G, let G? denote the character group of G. The group G is called reflexive if the evaluation map is a topological isomorphism of G onto G??, and G is called strongly reflexive if all closed subgroups and quotient[...]texto impreso
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The Pontryagin duality theorem for locally compact abelian groups (briefly, LCA groups) has been the starting point for many different routes of research in Mathematics. From its appearance there was a big interest to extend it in a context broa[...]texto impreso
The Pontryagin duality Theorem for locally compact abelian groups (briey, LCA-groups) has been the starting point for many different routes of research in Mathematics. From its appearance there was a big interest to obtain a similar result in a [...]texto impreso
An Abelian topological group is called strongly reflexive if every closed subgroup and every Hausdorff quotient of the group and of its dual group are reflexive. In the class of locally compact Abelian groups (LCA) there is no need to define "st[...]texto impreso
An Abelian topological group is called strongly reflexive if every closed subgroup and every Hausdorff quotient of the group and of its dual group are reflexive. In the class of locally compact Abelian groups (LCA) there is no need to define "st[...]
