Weakly least integer closed groups View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2003-10

AUTHORS

Anthony W. Hager, Chawne M. Kimber, Warren Wm. McGovern

ABSTRACT

An archimedean lattice-ordered groupA with distinguished weak unit has the canonical Yosida representation as an ℓ-group of extended real-valued functions on a certain compact Hausdorff spaceY A. Such an ℓ-groupA is calledleast integer closed, orLIC (resp.,weakly least integer closed, orwLIC) if, in the representation,a ∈A implies [a] ∈A (resp., there isa′ ∈A witha′=[a] on a dense set inY A), where [r] ≡ the least integer greater than or equal tor. Earlier, we have studiedLIC groups, with an emphasis on their a-extensions. Here, we turn towLIC groups: we give an intrinsic (though awk-ward) characterization in terms of existence of certain countable suprema. This results also in an intrinsic characterization ofLIC, previously lacking. Also,wLIC is a hull class (whichLIC is not), and the hullwlA is “somewhere near” the projectable hullpA. The best comparison comes from a (somewhat novel) factoringpA=loc(wpA), wherewpA is the “weakly projectable” hull (defined here), andlocB is the “local monoreflection”; then,wpA≤wlA≤loc(wpA), andpA≤loc(wlA), while with a strong unit, all these coincide. Numerous examples and special cases are examined. More... »

PAGES

453

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02872765

DOI

http://dx.doi.org/10.1007/bf02872765

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1038304266


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