Topology Proceedings 33 (2009), pp. 29-39

On two problems concerning topological centers

Eli Glasner

Let G be an infinite discrete group and bG its Cech-Stone compactification. Using the well known fact that a free ultrafilter on an infinite set is nonmeasurable, we show that for each element p of the remainder bG\G, left multiplication L_p:bG→ bG is not Borel measurable. Next assume that G is abelian. Let D ⊂ l^∞(G) denote the subalgebra of distal functions on G and let D = G^D = |D| denote the corresponding universal distal (right topological group) compactification of G. Our second result is that the topological center of D (i.e., the set of p ∈ D for which L_p:D → D is a continuous map) is the same as the algebraic center and that for G = Z, this center coincides with the canonical image of G in D.

Keywords: topological center, Cech-Stone compactification, Ellis group, distal systems

Mathematics Subject Classification: 54H20 (22A15)

Document formats: PDF file 175.7 Kb

Topology Proceedings, Volume 33 (2009)
Subscription information