  We prove that order convergence on a Boolean algebra turns it into a compact
convergence space if and only if this Boolean algebra is complete and atomic.
We also show that on an Archimedean vector lattice, order intervals are compact
with respect to order convergence if and only the vector lattice is complete
and atomic. Additionally we provide a direct proof of the fact that uo
convergence on an Archimedean vector lattice is induced by a topology if and
only if the vector lattice is atomic.
