Non-productive duality properties of topological groups

Details Non-productive duality properties of topological groups Non-productive duality properties of topological groups

2001-06-13

arxiv.org/abs/math/0106103v1

Mathematics

General Topology

6 pages

Scientific paper

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.

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