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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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Skew compact semigroups.
by
Ralph Kopperman
City College of CUNY

A topology on a set X is skew compact if there is a second topology on X so that the join of the two is compact, and each is Hausdorff with respect to the other (details in [1]); the second is called the dual of the first. The compact Hausdorff topologies are precisely the skew compact topologies which equal their duals. NonHausdorff skew compact topologies include:

Much of the theory of compact Hausdorff semigroups extends to skew compact semigroups with natural assumptions on continuity of the operation. For example, if the operation is continuous with respect to both topologies on a cancellative semigroup, it is a compact Hausdorff topological group. We will discuss a variety of such results, with various assumptions.

Much of this work is joint with Desmond Robbie. This talk should serve as an introduction to some of the concepts used in Neil Hindman's discussion on order compactifications of discrete semigroups.

Date received: May 25, 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 Conferences Inc. Document # cait-23.