The Concept of Boundedness and the Bohr Compactification of a MAP Abelian Group
by
Jorge Galindo
Coauthors: Salvador Hernandez

Let G be a MAP Abelian group and let B be a boundedness 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), 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: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caah-20.