On the continuity of left translations in the LUC-compactification

Consider the continuity of left translations in the LUC-compactitication G(LUC) of a locally compact group G. For every X subset of G, let kappa(X) be the minimal cardinality of a compact covering of X in G. Let U(G) be the points in G(LUC) that are not in the closure of any X subset of G with kappa(X) < kappa(G), We show that the points at which no left translation in U(G) is continuous are dense in U(G). This result is a generalization of a theorem by van Douwen concerning discrete groups. We obtain a new proof for the fact that the topological center of G(LUC) \ G is empty. (C) 2005 Elsevier B.V. All rights reserved.