Mathematics Faculty Articles

Title

On Hull Classes of l-groups and Covering Classes of Spaces

Document Type

Article

Publication Date

6-1-2011

Publication Title

Mathematica Slovaca

Keywords

Lattice-ordered groups, Essential extension, Hull, Hull class, Preserve boundedness, Anti-PB, Compact space, Cover, Covering class

ISSN

0139-9918

Volume

61

Issue/No.

3

First Page

411

Last Page

428

Abstract

W denotes the category of archimedean -groups with designated weak unit and -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 -groups.

DOI

10.2478/s12175-011-0020-7

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