Sublattices
A sublattice of a lattice L is a nonempty subset of L that is a lattice with the same meet and join operations as L. That is, if L is a lattice and M is a subset of L such that for every pair of elements a, b in M both ab and ab are in M, then M is a sublattice of L.
A sublattice M of a lattice L is a convex sublattice of L, if x ≤ z ≤ y and x, y in M implies that z belongs to M, for all elements x, y, z in L.
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