Finer closed left ideal decompositions of G~*

摘要

Let G be a countably infinite discrete group and let βG be the Stone-Cech compactification of G. Let (I) denote the finest decomposition of G~* = βG G into closed left ideals of βG with the property that the corresponding quotient space of G~* is Hausdorff, and (I') the finest decomposition of G~* into closed left ideals of βG. We show that there is a dense subset of points p ∈ G~* such that (βG)p ∈(I')(I) In particular, (I') is finer than (I).