Monoreflections of archimedean -groups, regular σ-frames and regular Lindelöf frames
نویسنده
چکیده
We prove that in the category of achimedean 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 σframes, 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 nontrivial 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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