On the continuity of separately continuous bihomomorphisms

TL;DR

This paper investigates conditions under which separately continuous bihomomorphisms on product groups become jointly continuous, leveraging Banach-Steinhaus type results and the advantages of convergence group structures.

Contribution

It provides new Banach-Steinhaus type theorems and demonstrates joint continuity of bihomomorphisms in convergence groups, expanding classical results.

Findings

Joint continuity derived from separate continuity under new conditions

Banach-Steinhaus type theorems adapted for convergence groups

Enhanced duality arguments using continuous convergence structures

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.