Joint continuity of separately continuous mappings on topological groups

Abstract

The main theorem of this paper is somewhat stronger than the following statement: Let G G be a Baire semitopological group, let H H be a first countable one and let N N be a first countable topological group; then each separately continuous bi-homomorphism from G × H G\times H into N N is jointly continuous. This theorem has some consequences on joint continuity of separately continuous multiplication of rings and scalar multiplication of modules.