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The concept of boundedness and the Bohr compactification of a MAP Abelian group

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Galindo J., Hernández S.

Fundamenta Mathematicae

1999

tom 159

nr 3

195-218

Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an $ℒ_∞$-group, contains "many" discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This result generalizes an analogous theorem of van Douwen for the discrete case and some other ones due to Hartman and Ryll-Nardzewski concerning the existence of $I_0$-sets. We also obtain some results on preservation of compactness for the Bohr topology of several types of MAP Abelian groups, like $ℒ_∞$-groups, locally convex vector spaces and free Abelian topological groups.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Galindo J.

1 Hernández S.

1 1999

Wyniki wyszukiwania

The concept of boundedness and the Bohr compactification of a MAP Abelian group