Glossary of Order Theory - W

W

• Way-below relation. In a poset P, some element x is way below y, written x<<y, if for all directed subsets D of P which have a supremum, y ≤ sup D implies x ≤ d for some d in D. One also says that x approximates y. See also domain theory.

• Weak order. A partial order ≤ on a set X is a weak order provided that the poset (X, ≤) is isomorphic to a countable collection of sets ordered by comparison of cardinality.