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A characterization of the maximally almost periodic abelian groups
- Source :
-
Journal of Pure & Applied Algebra . May2005, Vol. 197 Issue 1-3, p23-41. 19p. - Publication Year :
- 2005
-
Abstract
- Abstract: We introduce a categorical closure operator 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 -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). [Copyright &y& Elsevier]
- Subjects :
- *ABELIAN groups
*GROUP theory
*LATTICE theory
*CLOSURE operators
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 197
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 17465474
- Full Text :
- https://doi.org/10.1016/j.jpaa.2004.08.021