International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 207016, 18 pages
doi:10.1155/2008/207016

The characterizations of extreme amenability of locally compact semigroups

Abstract

We demonstrate that the characterizations of topological extreme amenability. In particular, we prove that for every locally compact semigroup S with a right identity, the condition μ⊙(F×G)=(μ⊙F)×(μ⊙G), for F, G in M(S)∗, and 0<μ∈M(S), implies that μ=εa, for some a∈S (εa is a Dirac measure). We also obtain the conditions for which M(S)∗ is topologically extremely left amenable.