  Let $(G,u)$ be an archimedean norm-complete dimension group with order unit.
Continuing a previous paper, we study intervals (i.e., nonempty upward directed
lower subsets) of $G$ which are closed with respect to the canonical norm of
$(G,u)$. In particular, we establish a canonical one-to-one correspondence
between closed intervals of $G$ and certain affine lower semicontinuous
functions on the state space of $(G,u)$, which allows us to solve several
problems of K. R. Goodearl about inserting affine continuous functions between
convex upper semicontinuous and concave lower semicontinuous functions. This
yields in turn new results about analogues of multiplier groups for norm-closed
intervals.
