  We characterize those join semilattices with a multicontact relation which
can be embedded into (the reduct of) a Boolean algebra with multicontact given
by overlap, equivalently, into a distributive lattice with additive
multicontact, still equivalently, into the multicontact semilattice associated
to some topological space. A similar characterization is presented for
embeddability into Boolean algebras or distributive lattices with a not
necessarily overlap nor additive multicontact.
