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In mathematics, a join-semilattice ( or upper semilattice ) is a partially ordered set which has a join ( a least upper bound ) for any nonempty finite subset.

Dually, a meet-semilattice ( or lower semilattice ) is a partially ordered set which has a meet ( or greatest lower bound ) for any nonempty finite subset.

Every join-semilattice is a meet-semilattice in the inverse order and vice versa.