Abstract
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. © 2011 Versita Warsaw and Springer-Verlag Wien.
Original language | American English |
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Pages (from-to) | 411-428 |
Number of pages | 18 |
Journal | Mathematica Slovaca |
Volume | 61 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1 2011 |
ASJC Scopus Subject Areas
- General Mathematics
Keywords
- Anti-PB
- Compact space
- Cover
- Covering class
- Essential extension
- Hull
- Hull class
- Lattice-ordered groups
- Preserve boundedness
- lattice-ordered groups
- compact space
- cover
- preserve boundedness
- covering class
- hull class
- anti-PB
- essential extension
- hull
Disciplines
- Mathematics