On hull classes of ℓ-groups and covering classes of spaces

Mathematica Slovaca

Ricardo Carrera¹  Anthony Hager¹ 

关键词: lattice-ordered groups;    essential extension;    hull;    hull class;    preserve boundedness;    anti-PB;    compact space;    cover;    covering class;   

DOI  :  10.2478/s12175-011-0020-7

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

W denotes the category of archimedean ℓ-groups with designated weak unit and ℓ-homomorphisms that preserve the weak unit. Comp denotes the category of compact Hausdorff spaces with continuous maps. The Yosida functor is used to investigate the relationship between hull classes in W and covering classes in Comp. The central idea is that of a hull class whose hull operator preserves boundedness. We demonstrate how the Yosida functor may be used to identify hull classes in W and covering classes in Comp. In addition, we exhibit an array of order preserving bijections between certain families of hull classes and all covering classes, one of which was recently produced by Martínez. Lastly, we apply our results to answer a question of Knox and McGovern about the class of all feebly projectable ℓ-groups.

【 授权许可】

Unknown