en.wikipedia.org/wiki/Directed_set

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 ...

ncatlab.org/nlab/show/direction

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 ...

mathworld.wolfram.com/DirectedSet.html

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 ...

thales.doa.fmph.uniba.sk/sleziak/texty/rozne/topo/subnets2.pdf

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.

www.encyclopediaofmath.org/index.php/Directed_set

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 ...

planetmath.org/directedset

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 ...

math.stackexchange.com/questions/135523/example-of-directed-set-directed-towards-x-0

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)." ...

math.stackexchange.com/questions/446685/can-directed-set-be-finite

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?)

encyclopedia2.thefreedictionary.com/Upward-directed set

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 ...

www.ams.org/tran/1985-290-02/S0002-9947-1985-0792822-9/S0002-9947-1985-0792822-9.pdf

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.