In
mathematics, a
directed set (or a
directed preorder or a
filtered set) is a nonempty
set A together with a
reflexive and
transitive binary relation = (that is, a
preorder), with the additional property that every pair of elements has an
upper bound. In other words, for any
a and
b in
A there must exist a
c in
A with
a =
c and
b =
c.