Each second countable abelian group is a subgroup of a second countable divisible group

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dc.creatorBanakh, T.
dc.creatorZdomskyy, L.
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:54Z
dc.date.available2026-07-07T10:10:54Z
dc.descriptionIt is shown that each pseudonorm defined on a subgroup $H$ of an abelian group $G$ can be extended to a pseudonorm on $G$ such that the densities of the obtained pseudometrizable topological groups coincide. We derive from this that any Hausdorff $ω$-bounded group topology on $H$ can be extended to a Hausdorff $ω$-bounded group topology on $G$. In its turn this result implies that each separable metrizable abelian group $H$ is a subgroup of a separable metrizable divisible group $G$. This result essentially relies on the Axiom of Choice and is not true under the Axiom of Determinacy (which contradicts to the Axiom of Choice but implies the Countable Axiom of Choice).
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/0810.3030
dc.identifierhttp://arxiv.org/abs/0810.3030
dc.identifierAlgebraical Structures and their Applications, Kyiv: Inst. Mat. NANU, (2002) 154-159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171726
dc.subjectGeneral Topology
dc.subjectGroup Theory
dc.subject22A05
dc.titleEach second countable abelian group is a subgroup of a second countable divisible group
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