The characterizations of extreme amenability of locally compact semigroups (Q1008543)

Summary: We demonstrate characterizations of topological extreme amenability. In particular, we prove that for every locally compact semigroup \(S\) with a right identity, the condition \(\mu \odot (F\times G)=(\mu \odot F)\times (\mu \odot G)\), for \(F, G\) in \(M(S^*)\), and \(0<\mu \in M(S)\), implies that \(\mu =\varepsilon _{a}\) for some \(a\in S\) \((\varepsilon _{a}\) is a Dirac measure). We also obtain conditions for which \(M(S^*)\) is topologically extremely left amenable.