The concept of boundedness and the Bohr compactification of a MAP Abelian group
Fundamenta Mathematicae, Tome 159 (1999) no. 3, pp. 195-218
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
Bohr topology, LCA group, $ℒ_∞$-group, boundedness, locally convex vector space, DF-space, maximally almost periodic, respects compactness, C-embedded, C*-embedded
Affiliations des auteurs :
Jorge Galindo 1 ; Salvador Hernández 1
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author = {Jorge Galindo and Salvador Hern\'andez},
title = {The concept of boundedness and the {Bohr} compactification of a {MAP} {Abelian} group},
journal = {Fundamenta Mathematicae},
pages = {195--218},
year = {1999},
volume = {159},
number = {3},
doi = {10.4064/fm-159-3-195-218},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-159-3-195-218/}
}
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Jorge Galindo; Salvador Hernández. The concept of boundedness and the Bohr compactification of a MAP Abelian group. Fundamenta Mathematicae, Tome 159 (1999) no. 3, pp. 195-218. doi: 10.4064/fm-159-3-195-218
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