On representation of semigroups of inclusion hyperspaces - Gavrylkiv, V.M. (Carpathian Mathematical Publications, 2010)
Given a group X we study the algebraic structure of the compact right-topological semigroup G(X) consisting of inclusion hyperspaces on X. This semigroup contains the semigroup λ(X) of maximal linked systems as a closed subsemigroup. We construct a faithful representation of the semigroups G(X) and λ(X) in the semigroup P(X)^P(X) of all self-maps of the power-set P(X). Using this representation we prove that each minimal left ideal of λ(X) is topologically isomorphic to a minimal left ideal of the semigroup pT^pT , where by pT we denote the family of pretwin subsets of X.