The yosida space of the vector lattice hull of an archimedean ℓ-group with unit

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W is the category of archimedean ℓ-groups with distinguished weak order unit. For G ϵ W, we have the contravariantly functorial Yosida space YG. For an embedding G ≤ H; the resulting YG → YH is surjective; when this is one-to-one, we write "YH = YG". This is the case with the divisible hull G ≤ dG, where, always, YdG = YG; however for the vector lattice hull G ≤ vG, we frequently have YvG ≠ YG. Theorem. A compact space X is quasi-F if and only if: ∀G ϵ W with YG = X, also YvG = X. ("quasi-F" means each dense cozero set is C-embedded.)

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Houston Journal of Mathematics

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