Comfort, W.W.Raczkowski, S.U.Trigos-Arrieta, F.J.2017-06-162017-06-162006-04-011576-9402https://riunet.upv.es/handle/10251/82968[EN] (1) Every infinite, Abelian compact (Hausdorff) group K admits 2|K|- many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a family A of 22|G|-many pairwise nonhomeomorphic totally bounded group topologies such that no nontrivial sequence in G converges in any of the topologies T ϵ A. (For some G one may arrange ω(G, T ) < 2|G| for some T ϵ A.) (3) Every infinite Abelian group G admits a family B of 22|G|-many pairwise nonhomeomorphic totally bounded group topologies, with ω (G, T ) = 2|G| for all T ϵ B, such that some fixed faithfully indexed sequence in G converges to 0G in each T ϵ B.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Haar measureDual groupCharacterPseudocompact groupTotally bounded groupMaximal topologyConvergent sequenceTorsion-free groupTorsion groupTorsion-free rankp-rankp-adic integersArtículo2017-06-1610.4995/agt.2006.1936Abierto1989-4147