  To a significant extent, the metrical and topological properties of spacetime
can be described purely order-theoretically. The $K^+$ relation has proven to
be useful for this purpose, and one could wonder whether it could serve as the
primary causal order from which everything else would follow. In that
direction, we prove, by defining a suitable order-theoretic boundary of
$K^+(p)$, that in a $K$-causal spacetime, the manifold-topology can be
recovered from $K^+$. We also state a conjecture on how the chronological
relation $I^+$ could be defined directly in terms of $K^+$.
