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We prove that in the character group of an abelian topological group, the topology associated (in a standard way) to the continuous convergence structure is the finest of all those which induce the topology of simple convergence on the correspon[...]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
Bruguera Padró, M. Montserrat ; Martín Peinador, Elena ; Tarieladze, Vaja | Oxford University Press | 2004Leaning on a remarkable paper of Pryce, the paper studies two independent classes of topological Abelian groups which are strictly angelic when endowed with their Bohr topology. Some extensions are given of the Eberlein–?Smulyan theorem for the [...]texto impreso
A number of attempts to extend Pontryagin duality theory to categories of groups larger than that of locally compact abelian groups have been made using different approaches. The extension to the category of topological abelian groups created th[...]
