Mathematics Faculty Articles

Title

B-saturated hull classes in l-groups and covering classes of spaces

Document Type

Article

Publication Date

10-1-2015

Publication Title

Applied Categorical Structures

Keywords

Lattice-ordered group, Weak unit, Essential extension, Hull class, Bounded coreflection, B-saturated, Compact space, Cover, Covering class, Yosida representation

ISSN

0927-2852

Volume

23

Issue/No.

5

First Page

709

Last Page

723

Abstract

W denotes the category of archimedean -groups with designated weak unit and -homomorphisms that preserve the weak unit, and B is the bounded coreflection in W. Comp denotes the category of compact Hausdorff spaces with continuous maps, and Y : W → Comp is the familiar Yosida functor. The enormous collection hcW of hull classes in W and the somewhat less enormous collection ccComp of covering classes in Comp are clearly related “via” Y, but rather unclearly in the details. In an earlier paper we investigated the relationship between hcW and ccComp and continue to do so here, now focusing on the role of B. Among other things, (i) we define B-saturated hull classes and the sub-species Y-saturated and type μ, (ii) show that for a hull class H of the latter two types, but not always the first, Y[H] is a covering class, and (iii) describe the various ways the three types relate. This paper is the second installment in our ongoing investigation of the complex taxonomy of hull classes.

DOI

10.1007/s10485-014-9376-5.