#### Title

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

#### Document Type

Article

#### Publication Date

1-1-2017

#### Abstract

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.)

#### Publication Source (Journal or Book title)

Houston Journal of Mathematics

#### First Page

1019

#### Last Page

1030

#### Recommended Citation

Ball, R., Hager, A., Johnson, D., Madden, J., & McGovern, W.
(2017). The yosida space of the vector lattice hull of an archimedean ℓ-group with unit.* Houston Journal of Mathematics**, 43* (3), 1019-1030.
Retrieved from https://repository.lsu.edu/mathematics_pubs/857