Continuous functions on locally pseudocompact groups

In this paper we explore the relation between locally pseudocompact groups and bƒ-spaces. Namely, we point out that bƒ-continuous functions appear in a natural way when studying the exponential map. We introduce the concept of bƒ-group and we prove that Σ-spaces of an arbitrary product of locally pseudocompact groups are bƒ-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 bƒ-groups is a bƒ-group.