The projectable hull of an archimedean ℓ-group with weak unit

The much-studied projectable hull of an ℓ-group G  pG is an essential extension, so that, in the case that G is archimedean with weak unit, “G 2 W”, we have for the Yosida representation spaces a “covering map” Y G Y pG. We have earlier [8] shown that (1) this cover has a characteristic minimality property, and that (2) knowing Y pG, one can write down pG. We now show directly that for A , the boolean algebra in the power set of the minimal prime spectrum Min(G), generated by the sets U(g) = {P 2 Min(G) : g /2 P} (g 2 G), the Stone space SA is a cover of Y G with the minimal property of (1); this extends the result from [1] for the strong unit case. Then, applying (2) gives the pre-existing description of pG, which includes the strong unit description of [1]. The present methods are largely topological, involving details of covering maps and Stone duality.