On the continuity of separately continuous bihomomorphisms

Details On the continuity of separately continuous bihomomorphisms On the continuity of separately continuous bihomomorphisms

2008-05-18

arxiv.org/abs/0805.2730v1

Mathematics

Functional Analysis

Scientific paper

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.

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