Contact semilattices
arXiv:2303.06787 · doi:10.1093/jigpal/jzad012
Abstract
We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.
v3: noticed that former Condition (D2-) is pleonastic; added two new equivalent conditions in Theorem 3.2. We realized all this after the paper has been published: variations with respect to the published version are printed in a blue character. v2: solved a problem left open in v1; added a counterexample; a few fixes