Definition
Let X be a set with a partial order ≤. As usual, let < be the relation on X such that x < y if and only if x ≤ y and x ≠ y.
Let x and y be elements of X.
Then y covers x, written x <· y, if x < y and there is no element z such that x < z < y. Equivalently, y covers x if the interval is the two-element set {x, y}.
When x <· y, it is said that y is a cover of x. Some authors also use the term cover to denote any such pair (x, y) in the covering relation.
Read more about this topic: Covering Relation
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