Article

The Yosida space and representation of the projectable hull of an archimedean ℓ-group with weak unit

Published in: Quaestiones Mathematicae
Volume 40 , issue 1 , 2017 , pages: 57–61

DOI: 10.2989/16073606.2017.1280710

Author(s): Anthony W. Hager Department of Mathematics and CS, USA , Warren Wm. McGovern H.L. Wilkes Honors College, USA

Keywords: Primary: 06F20 , 46A40 , Secondary: 54D35 , Primary: 06F20 , 46A40 , Secondary: 54D35

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Abstract

W is the category of archimedean ℓ-groups with designated weak order unit. The full subcategory of W of objects for which the unit is strong unit is denoted by W^∗; such ℓ-groups are called bounded. Thus arises a coreflection . For G ∈W, Y G is the Yosida space, and G ≤ pG is the much-studied projectable hull. Recently, in [1], for G ∈ W^∗, Y pG is identified as the Stone space of a certain boolean algebra of subsets of the minimal prime spectrum Min(G), and skepticism is expressed about extending this to W. Here, we show that indeed such an extension is possible, using a result from [5] and the following simple facts: in very concrete ways Min(G) and Min(BG) are homeomorphic spaces, and and are isomorphic boolean algebras; p and B commute.

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