Abstract
Arch denotes the category of archimedean ℓ-groups and ℓ-homomorphisms. Tych denotes the category of Tychonoff spaces with continuous maps, and α denotes an infinite cardinal or ∞. This work introduces the concept of an αcc-disconnected space and demonstrates that the class of αcc-disconnected spaces forms a covering class in Tych. On the algebraic side, we introduce the concept of an αcc-projectable ℓ-group and demonstrate that the class of αcc-projectable ℓ-groups forms a hull class in Arch. In addition, we characterize the αcc-projectable objects in W—the category of Arch-objects with designated weak unit and ℓ-homomorphisms that preserve the weak unit—and construct the αcc-hull for G in W. Lastly, we apply our results to negatively answer the question of whether every hull class (resp., covering class) is epireflective (resp., monocoreflective) in the category of W-objects with complete ℓ-homomorphisms (resp., the category of compact Hausdorff spaces with skeletal maps).
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Presented by W. McGovern.
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Carrera, R.E. Various disconnectivities of spaces and projectabilities of ℓ-groups. Algebra Univers. 68, 91–109 (2012). https://doi.org/10.1007/s00012-012-0198-8
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DOI: https://doi.org/10.1007/s00012-012-0198-8