A characterization of the maximally almost periodic abelian groups

We introduce a categorical closure operator g in the category of topological abelian groups (and continuous homomorphisms) as a Galois closure with respect to an appropriate Galois correspondence defined by means of the Pontryagin dual of the underlying group. We prove that a topological abelian gro...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2005-05, Vol.197 (1), p.23-41
Main Authors: Dikranjan, Dikran, Milan, Chiara, Tonolo, Alberto
Format: Article
Language:English
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Summary:We introduce a categorical closure operator g in the category of topological abelian groups (and continuous homomorphisms) as a Galois closure with respect to an appropriate Galois correspondence defined by means of the Pontryagin dual of the underlying group. We prove that a topological abelian group G is maximally almost periodic if and only if every cyclic subgroup of G is g -closed. This generalizes a property characterizing the circle group from (Studia Sci. Math. Hungar. 38 (2001) 97–113, A characterization of the circle group and the p-adic integers via sequential limit laws, preprint), and answers an appropriate version of a question posed in (A characterization of the circle group and the p-adic integers via sequential limit laws, preprint).
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2004.08.021