Countably Indicated Uniform Convergence on Archimedean Lattice-Ordered Groups with Weak Unit
by
Richard N. Ball
University of Denver
Coauthors: Anthony W. Hager (Wesleyan University)

(This talk will follow Professor Hager's talk, and we refer the reader of this abstract to Hager's for motivation, terminology, and background. What distinguishes the two talks is that Hager will be concerned with singly indicated uniform convergence, whereas this talk will be concerned with countably indicated uniform convergence.) We introduce a variant of uniform convergence, here termed countably indicated uniform convergence, and show that it behaves very nicely on W-objects; for example, it is Hausdorff and renders the group and lattice operations continuous. But what makes this convergence especially nice is that it combines two important features. For an extension A <= B, density of A in B with respect to this convergence is equivalent to the embedding being an epimorphism in W. And the associated Cauchy completion of A is the largest essential monoreflection c³A of A. This convergence is the direct limit of topologies, each of which can be viewed as a restricted form of the compact-open topology on A.

Date received: January 31, 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 # cain-12.