  We demonstrate the equivalence of two classes of $D$-invariant polynomial
subspaces introduced in [8] and [9], i.e., these two classes of subspaces are
different representations of the breadth-one $D$-invariant subspace. Moreover,
we solve the discrete approximation problem in ideal interpolation for the
breadth-one $D$-invariant subspace. Namely, we find the points, such that the
limiting space of the evaluation functionals at these points is the functional
space induced by the given $D$-invariant subspace, as the evaluation points all
coalesce at one point.
