International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 493-502

Thickness in topological transformation semigroups

Tyler Haynes

Mathematics Department, Saginaw Valley State University, University Center 48710-0001, Michigan, USA

Received 27 June 1989; Revised 5 February 1993

Copyright © 1993 Tyler Haynes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.