Pseudocompact Totally Dense Subgroups
نویسندگان
چکیده
It was shown by Dikranjan and Shakhmatov in 1992 that if a compact abelian group K admits a proper totally dense pseudocompact subgroup, then K cannot have a torsion closed Gδ-subgroup; moreover this condition was shown to be also sufficient under LH. We prove in ZFC that this condition actually ensures the existence of a proper totally dense subgroup H of K that contains an ω-bounded dense subgroup of K (such an H is necessarily pseudocompact). This answers two questions posed by Dikranjan and Shakhmatov (Proc. Amer. Math. Soc. 114 (1992), 1119–1129).
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