Local Topological Structure in the LUC-Compactification of a Locally Compact Group and its Relationship with Veech's Theorem

Abstract

The paper begins by presenting a construction of the largest semigroup compactification GLUC of a locally compact group as a quotient of the Stone-Cech compactification of the discrete group βGd. This presentation is used in a proof of the local structure theorem for GLUC, which gives a topological description of neighbourhoods of each point, and some new extensions of this result. These immediately imply Veech's Theorem. Finally a result is given which extends Veech's Theorem: for σ-compact groups the map g → gx is injective for all x ∈ GLUC on a set larger than G.