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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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Order compactifications of discrete semigroups
by
Neil Hindman
Howard University
Coauthors: Ralph Kopperman (CCNY)

Given a partially ordered set (X, <= ) we construct the order compactification \muX of X in the same fashion as Cech's construction of the Stone-Cech compactification, using the order preserving functions from X into the unit interval [0, 1]. We present some of the elementary properties of this compactification. We then consider a semigroup (S, ·) which has an ordering which the semigroup respects in the sense that x <= y implies that z·x <= z·y and x·z <= y·z for all x, y, z in S. We show that the operation can be extended to \muS making it into a right topological semigroup with S contained in the topological center such that both the left and right translations are order preserving. We then investigate the structure of \muS for certain specific semigroups S.

Date received: June 10, 2002

Copyright © 2002 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 Mathematical Conference Abstracts. Document # cait-40.