On epicomplete archimedean l-groups
by
Anthony W. Hager
Wesleyan University
Coauthors: Richard N. Ball, Ann Kizanis, Donald G. Johnson

In a category, an object A is called epicomplete (ec) if the only epic embeddings of A are isomorphisms (epic in the categorical sense of right-cancellable). In Arch (archimedean l-groups) and in W (Arch-objects with weak unit),A is ec iff A is divisible, and both conditionally and laterally sigma-complete;and in each of Arch and W ,ec is monoreflective. In W a) A is ec iff A=D(Y) for Y compact and basically disconnected (bd),and b) the reflection of A is a certain quotient of the Baire functions on the Yosida space of A.

What about Arch? a) The working conjecture is that A is ec iff A=D(Y,p)={f in D(Y): f(p)=0}, for compact bd Y with P-point p. We prove this in case A is the l-group part of a semi-prime arch. f-ring (using a representation of Johnson),and in case A has a disjoint subset which generates A as an arch. kernel. b) We give a representation of the ec-reflection of A as a subdirect product of W-ec objects derived from A. This permits an explicit calculation of the ec-reflection of the l-group of continuous functions of compact support on a sum of compacta,as a certain l-group of Baire functions. (One would like to do better.)

Date received: December 6, 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 # cakg-04.