| Suppose (L0,≤) is a poset (i.e. partially ordered set) with an order reversing involution λ→λ′ and has an all element 1. Let L={b|b is a subset of L0 and satisfies the condition: if λ∈b,μ≤λ then μ∈b} then (L,?,∩,∪) is a complete and distributive lattice. L is called the lattice induced from poset L0. There is a mapping α→a′={λ∈L0|λ′(?)a} of a lattice L onto L. The mapping is clearly order reversing involution. |
