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Article
On Hull Classes of l-groups and Covering Classes of Spaces
Mathematica Slovaca
  • Ricardo Enrique Carrera, Nova Southeastern University
  • Anthony W. Hager, Wesleyan University
Document Type
Article
Publication Date
6-1-2011
Keywords
  • Lattice-ordered groups,
  • Essential extension,
  • Hull,
  • Hull class,
  • Preserve boundedness,
  • Anti-PB,
  • Compact space,
  • Cover,
  • Covering class
Disciplines
Peer Reviewed
1
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.
DOI
10.2478/s12175-011-0020-7
Citation Information
Ricardo Enrique Carrera and Anthony W. Hager. "On Hull Classes of l-groups and Covering Classes of Spaces" Mathematica Slovaca Vol. 61 Iss. 3 (2011) p. 411 - 428 ISSN: 0139-9918
Available at: http://works.bepress.com/ricardo-carrera/18/