Epimorphic Adjunction of a Weak Order Unit to an Archimedean Lattice-Ordered Group

Ball, Richard N.; Hager, Anthony W.; Kizanis, Ann

doi:10.2307/2159733

Cited by 2 publications

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“…(g) To recognize a βG from 3.2, in some specific cases there may be a virtue in minimizing the cardinal number |U |. The case |U | = 1 is mentioned in (b) above, and there is information about the case |U | = ω in [9]. For G = C K (Y ), which is discussed in the next section, it is not hard to see that the minimum |U | is the so-called Lindelöf degree L (Y ) (see [13]), but we see no value in this observation.…”

Section: Vol 54 2005mentioning

confidence: 99%

On the epicomplete monoreflection of an archimedean lattice-ordered group

et al. 2005

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In a category C an object G is epicomplete if the only epic monics out of G are isomorphisms, epic or monic meant in the categorical sense of right or left cancellable. For each of the categories Arch: archimedean -groups with -homomorphisms, and its companion category W: Arch-objects with distinguished weak unit and unit-preserving -homomorphisms, (and for the corresponding categories of vector lattices) epicompleteness has been characterized as divisible and conditionally and laterally σ-complete, and it has been shown to be monoreflective.Denote the reflecting functors by β and β W , respectively. What are they? For W the Yosida representation has been used to realize β W A as a certain quotient of B (Y A), the Baire functions on the Yosida space of A. For Arch, very little has been known. Here we give a general representation theorem, Theorem A, for βG as a certain subdirect product of W -epicomplete objects derived from G. That result, some W -theory, and the relation between epicity and relative uniform density are then employed to show Theoremis the -group of continuous functions on Y with compact support and B L (Y ) is the -group of Baire functions on Y having Lindelöf cozero sets.

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Section: Vol 54 2005mentioning

confidence: 99%