Title

Monoreflections of Archimedean ℓ-groups, regular σ-frames and regular Lindelöf frames

Document Type

Article

Publication Date

10-1-2006

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. © 2005 Elsevier B.V. All rights reserved.

Publication Source (Journal or Book title)

Topology and its Applications

First Page

3169

Last Page

3179

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