Abstract
The result of the title is: an archimedean $$\ell $$ -group with weak unit A is (isomorphic to) $$C(\mathcal {L})$$ for some (identifiable) locale $$\mathcal {L}$$ (or, $$\mathbb {R}\mathcal {L}^{\mathrm {op}}$$ , $$\mathcal {L}^{\mathrm {op}}$$ the opposite frame) iff A is divisible and “ $$*$$ -complete,” (a type of sequential completeness). This is from Ball and Hager (Positivity 10:165–199, 2006), and is revisited here, with streamlined proof.
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