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- W1615469968 abstract "We 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." @default.
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- W1615469968 date "2001-06-13" @default.
- W1615469968 modified "2023-09-27" @default.
- W1615469968 title "Non-productive duality properties of topological groups" @default.
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