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Title

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

Authors 1, 1

Affiliations

  1. Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain

Abstract

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 I0-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.

Keywords

ENG
Bohr topology, LCA group, ℒ∞-group, boundedness, locally convex vector space, DF-space, maximally almost periodic, respects compactness, C-embedded, C*-embedded

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Fundamenta Mathematicae
1999/159/3
Export to PBN, Opens in new tab
Pages:
195-218
Main language of publication
English
Received
1997-02-07
Accepted
1998-07-27
Published
1999
Exact and natural sciences