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Sixth Annual Conference in Ordered Algebraic Structures
March 5-8, 2003
Department of Mathematics, Vanderbilt University
Nashville, TN, USA

Organizers
Jorge Martinez, University of Florida and Constantine Tsinakis, Vanderbilt University

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Strongly Epicomplete T_0 Spaces
by
Eric R. Zenk
University of Florida

We say X is strongly epicomplete if each epic monomorphism (right and left cancellable continuous map )with domain X is a homeomorphism. We are interested in strongly epicomplete objects in connection with monoreflections of topological categories.

The presentation will give background and a discussion of the following theorem.

Theorem: For a T0 space X, the following are equivalent:
(i) X is strongly epicomplete.
(ii) f:X --> Y, injective implies f is an embedding; moreover b(f(X)) = f(X).
(iii) X is sober and has a minimal T0 topology.
(iv) X is sober, is a chain in the generalization order, and has the weakest T0 topology compatible with that order.

Date received: January 28, 2003

Copyright © 2003 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 # cakg-24.