The Hasse diagram of the power set of three elements, partially ordered by inclusion.

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.


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.