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 ...
Apr 22, 2009 ... book. 1 Directed sets and nets. We first recall some basic definitions. Definition
1.1. We say that (D, ≤) is a directed set, if ≤ is a relation on D.
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 ...
Aug 1, 2002 ... A directed set is a partially ordered set ( A ) A (A,\leq) such that whenever a ... We
may also define the dual notion: a downward-directed set (or ...
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)." ...
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?)
Looking for Upward-directed set? Find out information about Upward-directed set
. A partially ordered set with the property that for every pair of elements a,b in ...
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.