closure pair(s, f)s under a function f is that it is the smallest set containing s and closed under f. The following three propositions embody this characterization. The first says that it contains s, the second that it is closed under f, and the third that it is the smallest such set.The set s is a subset of closure pair(s, f).
The set closure pair(s, f) is closed under f.
If x is a superset of s and is closed under f then closure pair(s, f) is a subset of x.
up | previous | next | detailed contents | brief contents