Recent results on the Bohr topology of topological Abelian groups
by
Salvador Hernández
Universitat Jaume I

The Bohr topology of a topological group (G, \tau) is the topology that the group inherits as a subgroup of its Bohr compactification. In this talk we report on some recent results and questions around the Bohr topology of a topological Abelian group. For instance, one main problem is the identification of those properties on (G, \tau) that are invariant when passing to the Bohr topology of the group. Along this line, we comment on two pivotal results due to Glicksberg and, respectively, van Douwen about the preservation of compactness and, respectively, the existence of large discrete subsets. It will be shown how those two, in principle, quite different results are equivalent for a wide class of topological Abelian groups.

Paper reference: atlas:ideb-96

Date received: August 29, 2000