- Galois connection. Given two posets P and Q, a pair of monotone functions F:P → Q and G:Q → P is called a Galois connection, if F(x) ≤ y is equivalent to x ≤ G(y), for all x in P and y in Q. F is called the lower adjoint of G and G is called the upper adjoint of F.
- Greatest element. For a subset X of a poset P, an element a of X is called the greatest element of X, if x ≤ a for every element x in X. The dual notion is called least element.
- Ground set. The ground set of a poset (X, ≤) is the set X on which the partial order ≤ is defined.
Read more about this topic: Glossary Of Order Theory