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