Thickness in topological transformation semigroups

Abstract

This article deals with thickness in topological transformation semigroups (τ-semigroups). Thickness is used to establish conditions guaranteeing an invariant mean on a function space defined on a τ-semigroup if there exists an invariant mean on its functions restricted to a sub-τ-semigroup of the original τ-semigroup. We sketch earlier results, then give many equivalent conditions for thickness on τ-semigroups, and finally present theorems giving conditions for an invariant mean to exist on a function space.

Keywords

• thickness
• topological transformation semigroup
• transformation semigroup
• invariant mean.