Non-productive duality properties of topological groups

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dc.creatorHigasikawa, Masasi
dc.date2001-06-13
dc.date.accessioned2026-07-07T04:42:08Z
dc.date.available2026-07-07T04:42:08Z
dc.descriptionWe address two properties for Abelian topological groups: ``every closed subgroup is dually closed'' and ``every closed subgroup is dually embedded.'' We exhibit a pair of topological groups such that each has both of the properties and the product has neither, which refutes a remark of N. Noble. These examples are the additive group of integers topologized with respect to a convergent sequence as investigated by E.G. Zelenyuk and I.V. Protasov. The proof for the product relies on a theorem on exponential Diophantine equations.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0106103
dc.identifierhttp://arxiv.org/abs/math/0106103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61646
dc.subjectGeneral Topology
dc.subjectNumber Theory
dc.subject22A05, 43A40 (Primary) 11D61, 11Z05 Secondary
dc.titleNon-productive duality properties of topological groups
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