A set 
together with a relation 
which is both transitive
and reflexive such that for any two elements 
, there exists another element 
with 
and 
. In this case, the relation 
is said to "direct" the set.
Directed Set
See also
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Cite this as:
Weisstein, Eric W. "Directed Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirectedSet.html