1. (of a set S) A finite set of subsets of S whose union is just S itself. The subsets, A1, A2,…, Am, are said to cover S. If the elements Ai for i = 1, 2,…, m are mutually disjoint, then the covering
is called a
partition of
S.
2. A relationship between two elements of a partially ordered set S. If x and y are elements of S then y covers x if and only if x<y, and whenever x≤z≤y for some element z in S, then either x = z or z = y.