International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 493-502
doi:10.1155/S0161171293000602

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.