Inmathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is commonly used to graphically express the partial order by means of the Hasse diagram.
Let be a set with a partial order
.
As usual, let
be the relation on
such that
if and only if
and
.
Let and
be elements of
.
Then covers
, written
,
if
and there is no element
such that
. Equivalently,
covers
if the interval
is the two-element set
.
When , it is said that
is a cover of
. Some authors also use the term cover to denote any such pair
in the covering relation.
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