Some new results on totally bounded group topologies
by
Salvador Hernandez
Universitat Jaume I
Coauthors: Jorge Galindo

A well-known theorem of Varopoulos establishes that the topology of each compact (even locally compact) group is completely determined by its convergent sequences. However, this result is not longer true if we consider subgroups of compact groups (totally bounded groups). Indeed, there are many groups G, on which we can find different families of totally bounded group topologies with the same convergent sequences. In this talk, we give some sufficient conditions on any pair of totally bounded group topologies, \tau₁ and \tau₂ defined on a group G in order to deduce that (G, \tau₁) and (G, \tau₂) possesses the same convergent sequences. The results are applied to the study of the Bohr topology for several families of topological groups.

Date received: June 18, 2001