covering
1. of a set S. A finite set of subsets of S whose union is just S itself. The subsets, A₁, A₂,…, A_m, are said to cover S. If the elements A_i for i = 1, 2,…, m are mutually disjoint, then the covering {A₁,…A_m}

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.

cov·er·ing / ˈkəv(ə)ring/ • n. a thing used to cover something else, typically in order to protect or conceal it. ∎  [usu. in sing.] a layer of something that covers something else: a covering of cloud.