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

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.