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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Largest Proper ideals of Transformation Semigroups
by
K. D. Magill, Jr.
SUNY at Buffalo

Let T(X) be a transformation semigroup on the set X which contains a proper ideal and either a left identity, a right identity or an identity. Then T(X) has a largest proper ideal and in the main result, the functions in that ideal are explicitly described. This, and previous results are then applied in order to describe, when they exist, the largest proper ideal, the largest proper left ideal and the largest proper right ideal of various semigroups of continuous selfmaps of topological spaces. For example, let S(X) denote the semigroup of all continuous selfmaps of the topological space X and let e be any nonconstant idempotent of S(X). These ideals, when they exist, are explicitly described for the semigroups e o S(X), S(X) o e and e o S(X) o e.

Date received: April 12, 1996

Copyright © 1996 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 # caae-55.