In mathematics, a directed set is a nonempty set A together with a reflexive and
transitive binary relation ≤ (that is, a preorder), with the additional property that ...
Jun 22, 2014 ... A directed set is a set equipped with a direction. A directed poset is a directed set
whose preorder is a partial order (so directed proset might be ...
Directed Set. A set S together with a relation >= which is both transitive and
reflexive such that for any two elements a,b in S , there exists another element c
in S ...
A partially ordered set with the property that for every pair of elements a,b in the
set, there is a third element which is larger than both a and b. Also known as ...
Aug 1, 2002 ... A directed set is a partially ordered set ( A ) A (A,\leq) such that whenever a , b ∈
A a b A a,b\in A there is an x ∈ A x A x\in A such that a ≤ x a x ...
Oct 8, 2013 ... But I have also seen sets such as [ o , a ) used as examples of directed sets that
do not contain their supremum. My sense is that finite directed ...
Jul 19, 2016 ... Suppose P is a nonempty partially ordered set with no least element, like ( 0 , ∞ )
for example, and adjoin two incomparable minimums m 1 and ...
Jul 22, 2016 ... Is there a term for a structure ( S , ⪯ , + ) where + is commutative, idempotent, and
monotone with respect to ⪯ ? That is, for all elements s and t ,.
Jul 18, 2013 ... Can we have directed sets to be finite sets? How do we define nets on such sets?
How do we define clustering and convergence of such nets?
A directed set is a pair ( A , ≤ ) where ≤ is a reflexive, transitive relation such that
for any x , y ∈ A we have some z such that x , y ≤ z . (This comes up when ...