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 ...
Oct 14, 2014 ... A set A equipped with a directed order. A set A with partial order ≤ is called
upwards (respectively, downwards) directed if ≤ (respectively, the ...
directed sets of size S,, but that there exist many cofinal types of directed sets of ...
directed sets D and E are cofinally similar if there is a partially ordered set C in.
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 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 ...
Apr 22, 2012 ... We then say that the reals have been directed towards x 0 . This is an example of
a directed set that is not ordered (neither totally nor partially)." ...
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 18, 2013 ... Note that in a directed set every finite subset has an upper bound. If the directed
set itself is finite, then it must have a maximum (why?).