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On hull classes of $\ell$-groups and covering classes of spaces

In: Mathematica Slovaca, vol. 61, no. 3
Ricardo E. Carrera - Anthony W. Hager

Details:

Year, pages: 2011, 411 - 428
Keywords:
lattice-ordered groups, essential extension, hull, hull class, preserve boundedness, anti-PB, compact space, cover, covering class
About article:
$\mathbf{W}$ denotes the category of archimedean $\ell$-groups with designated weak unit and $\ell$-homomorphisms that preserve the weak unit. $\mathbf{Comp}$ denotes the category of compact Hausdorff spaces with continuous maps. The Yosida functor is used to investigate the relationship between hull classes in $\mathbf{W}$ and covering classes in $\mathbf{Comp}$. 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 $\mathbf{W}$ and covering classes in $\mathbf{Comp}$. 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 $\ell$-groups.
How to cite:
ISO 690:
Carrera, R., Hager, A. 2011. On hull classes of $\ell$-groups and covering classes of spaces. In Mathematica Slovaca, vol. 61, no.3, pp. 411-428. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0020-7

APA:
Carrera, R., Hager, A. (2011). On hull classes of $\ell$-groups and covering classes of spaces. Mathematica Slovaca, 61(3), 411-428. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0020-7
About edition: