Covering relation

In mathematics, 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.

be a set with a partial order

As usual, let

be elements of

covers

, written

and there is no element

Equivalently,

covers

if the interval

is the two-element set

is a cover of

Some authors also use the term cover to denote any such pair

in the covering relation.