Martín Peinador, ElenaBanaszczyk, W2023-06-202023-06-201999-05-170022-404910.1016/S0022-4049(98)00034-6https://hdl.handle.net/20.500.14352/57589Let G be an Abelian topological group and G(+) the group G endowed with the weak topology induced by continuous characters. We say that G respects compactness (pseudocompactness, countable compactness, functional boundedness) if G and G+ have the same compact (pseudocompact, countably compact, functionally bounded) sets. The well-known theorem of Glicksberg that LCA groups respect compactness was extended by Trigos-Arrieta to pseudocompactness and functional boundedness. In this paper we generalize these results to arbitrary nuclear groups, a class of Abelian topological groups which contains LCA groups and nuclear locally convex spaces and is closed with respect to subgroups, separated quotients and arbitrary products.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022404998000346http://www.sciencedirect.com/science/restricted access515.12locally compact Abelian groupnuclear groupsnuclear locally convex spacescompactnesscountable compactnesspseudocompactnessfunctional boundednessAbelian groupsTopología1210 Topología