Continuous functions on locally pseudocompact groups

Abstract

In this paper we explore the relation between locally pseudocompact groups and b ƒ- spaces . Namely, we point out that b ƒ- continuous functions appear in a natural way when studying the exponential map. We introduce the concept of b ƒ- group and we prove that Σ-spaces of an arbitrary product of locally pseudocompact groups are b ƒ- groups . We show that the Dieudonné topological completion of an arbitrary product of locally pseudocompact groups agrees with its bilateral completion and then it is a topological group. We also study the distribution of the functor of the Dieudonné topological completion for coset spaces and characterize when the product of two b ƒ- groups is a b ƒ- group .