On the continuity of separately continuous bihomomorphisms
Functional Analysis
2008-05-20 v1 Group Theory
Abstract
Separately continuous bihomomorphisms on a product of convergence or topological groups occur with great frequency. Of course, in general, these need not be jointly continuous. In this paper, we exhibit some results of Banach-Steinhaus type and use these to derive joint continuity from separate continuity. The setting of convergence groups offers two advantages. First, the continuous convergence structure is a powerful tool in many duality arguments. Second, local compactness and first countability, the usual requirements for joint continuity, are available in much greater abundance for convergence groups.
Cite
@article{arxiv.0805.2730,
title = {On the continuity of separately continuous bihomomorphisms},
author = {R. Beattie and H. -P. Butzmann},
journal= {arXiv preprint arXiv:0805.2730},
year = {2008}
}