  A remarkable result due to Kou, Liu & Luo states that the condition of
continuity for a dcpo can be split into quasi-continuity and meet-continuity.
Their argument contained a gap, however, which is probably why the authors of
the monograph Continuous Lattices and Domains used a different (and fairly
sophisticated) sequence of lemmas in order to establish the result. In this
note we show that by considering the Stone dual, that is, the lattice of
Scott-open subsets, a straightforward proof may be given. We do this by showing
that a complete lattice is prime-continuous if and only if it is
join-continuous and hypercontinuous. A pleasant side effect of this approach is
that the characterisation of continuity by Kou, Liu & Luo also holds for
posets, not just dcpos.
