Epi-topology and Epi-convergence for Archimedean Lattice-ordered Groups with Unit |
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Authors: | Richard N Ball Anthony W Hager |
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Institution: | (1) Department of Mathematics, University of Denver, Denver, CO 80208, USA;(2) Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, USA |
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Abstract: | is the category of archimedean -groups with distinguished weak order unit, with -group homomorphisms which preserve unit. This category includes all rings of continuous functions and all rings of measurable functions modulo null functions, with ring homomorphisms. The authors, and others, have studied
previously the epimorphisms (right-cancellable morphisms) in . There is a rich theory. In this paper, we describe a topological approach to the analysis of these epimorphisms. On each
– object, we define a topology and a convergence . These have the same closure operator, and this closure “captures epics” in the sense: a divisible subobject of is dense iff is epically embedded. The topology is , but only sometimes Hausdorff or an -group topology. The convergence is a Hausdorff -group convergence, but only sometimes topological. The associations of to , and to , are functorial.
Dedicated to Bernhard Banaschewski for his 80th birthday. |
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Keywords: | lattice-ordered group epimorphism topological group convergence group space with filter |
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