When is an IP set a \delta-IP set ?
by
Jillian McLeod
Howard University

A partial semigroup is a nonempty set S with an operation *, which is associative when it is defined. We discusss notions of size taken from Topological Dynamics. One of these notions is that of an IP set , which is combinatorially defined in an arbitrary semigroup as a set containing the set of finite distinct products from an infinite sequence and is algebraically characterized as a member of an idempotent in the Stone-Cech compactification \betaS of S. Both of these characterizations have natural analogues in partial semigroups. We establish that for a partial semigroup the algebraic characterization and combinatorial definition of an IP set are in general not equivalent. We consider conditons for which they are.

Date received: June 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-22.