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Usually, an abelian $\ell$-group, even an archimedean $\ell$-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 $\ell$-groups with weak unit which are “$\mathbb{Q}$-convex”. ($\mathbb{Q}$ is the group of rationals.) Any $C(X,\mathbb{Q})$ is $\mathbb{Q}$-convex and its unique $a$-closure is the Alexandroff algebra of functions on $X$ defined from the clopen sets; this is sometimes $C\left(X\right)$.