Monoreflections of Archimedean ?-groups, regular σ-frames and regular Lindelöf frames |
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Authors: | AW Hager JJ Madden |
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Institution: | a Department of Mathematics, Wesleyan University, Middletown, CT, USA b Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA |
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Abstract: | We prove that in the category of Archimedean lattice-ordered groups with weak unit there is no homomorphism-closed monoreflection strictly between the strongest essential monoreflection (the so-called “closure under countable composition”) and the strongest monoreflection (the epicompletion). It follows that in the category of regular σ-frames, the only non-trivial monoreflective subcategory that is hereditary with respect to closed quotients consists of the boolean σ-algebras. Also, in the category of regular Lindelöf locales, there is only one non-trivial closed-hereditary epi-coreflection. The proof hinges on an elementary lemma about the kinds of discontinuities that are exhibited by the elements of a composition-closed l-group of real-valued functions on R. |
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Keywords: | 06F25 54C30 18A40 |
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