Atlas: The concept of boundedness and the Bohr compactification of a MAP Abelian group by Salvador Hernandez

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The Curacao Comfort Conference on Set-Theoretic Topology
June 17-21, 1996

Curacao, Netherlands Antilles

Organizers
Anthony Hager

The concept of boundedness and the Bohr compactification of a MAP Abelian group
by
Salvador Hernández
Universitat Jaume I
Coauthors: Jorge Galindo

Let G be a MAP Abelian group and let \Cal B be a boundedness in the sense of Vilenkin. We study the relations between \Cal B and the Bohr topology of G for some well known groups with boundedness (G, \Cal B), obtaining some uniform boundedness results which generalize classical theorems such as Glicksberg's theorem on weakly compact subsets of a LCA group and the uniform boundedness principle on a locally convex vector space. As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a Banach space with separable dual and a LCA group, contains ``many" discrete C-embedded subsets which are C^*-embedded in its Bohr compactification. This result generalizes an analogous thorem of van Douwen for the discrete case.

Date received: May 31, 1996