Topological Dynamics and the Algebra of bS
by
Neil Hindman
Howard University

If S is an infinite discrete semigroup, then its Stone-Cech compactification, bS, has an interesting and useful algebraic structure (as anyone who has heard me speak in the last 20 years is aware). There are also several connections with notions and structures arising in the context of topological dynamics. For example, the notion of syndetic , which originated in topological dynamics as a description of almost periodicity, provides a concrete description of the members of the smallest ideal of bS. In the other direction, if L is a minimal left ideal of bS and for each s Î S, l_s:L® L is defined by l_s(q)=s·q, then (L, ál_sñ_{s Î S}) is a universal minimal dynamic system for S. These and several other connections between topological dynamics and the algebra of bS will be discussed.

Date received: January 21, 1998