Semigroups of nonlinear mappings with extreme amenability and Homology for graphs and twisted C*- Algebras

Abstract

We show the variational principles for topological entropies of subsets of a metric space. We established some fixed point properties for semigroups of nonlinear mappings and the extreme amenability of abelian topological groups. Homology theory for higher-rank graphs and twisted ∗ -Algebras are considered.