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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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More on Suitable Sets in Compact Semigroups
by
Desmond A. Robbie
University of Melbourne
Coauthors: Jian He (University of Melbourne), Karl Hofmann (Darmstadt and Tulane), Sally M. Miller (University of Melbourne)

A suitable set A in a topological semigroup S is a subset of S which contains no idempotents, any limit points of A in S are idempotents, and A, together with all idempotents of S, generates a dense subsemigroup of S. Following work of Hofmann and Morris, who showed that every compact Hausdorff topological group has such a suitable set, this paper extends that result to several classes of compact semigroups all of whose members satisfy S2=S. In particular all compact simple semigroups are shown to have a suitable set. Cartesian products of compact monoids each with a suitable set have suitable sets as do continuous homomorphic images of compact semigroups with suitable sets. It is shown that certain classes of \EuScriptH-chain semigroups have suitable sets. The class of irreducible semigroups falls into two classes, where the members of one class always have a suitable set and in the other class a semigroup which contains no suitable set is constructed. It is shown that compactifications of subsemigroups of Lie groups tend to have suitable sets; these include the `triangle semigroup' as a typical test case. If S is compact, connected, and S2 =/= S, then S cannot have a suitable set.

Date received: June 15, 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-43.