Abstract
Usually, an abelian l-group, even an archimedean l-group, has a relatively large infinity of distinct a-closures. Here, we find a reasonably large class with unique and perfectly describable a-closure, the class of archimedean l-groups with weak unit which are “ℚ-convex”. (ℚ is the group of rationals.) Any C(X, ℚ) is ℚ-convex and its unique a-closure is the Alexandroff algebra of functions on X defined from the clopen sets; this is sometimes C(X).
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