Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology

摘要

In this paper we introduce perfectly supportable semigroupsand prove that they are σ-discrete in each Hausdorff shiftinvarianttopology. The class of perfectly supportable semigroupsincludes each semigroup S such that FSym(X) ? S ?FRel(X) where FRel(X) is the semigroup of finitely supportedrelations on an infinite set X and FSym(X) is the group offinitely supported permutations of X.