Collectionwise normal space

In mathematics, a topological space is called collectionwise normal if for every discrete family F_i (i ∈ I) of closed subsets of there exists a pairwise disjoint family of open sets U_i (i ∈ I), such that F_i ⊂ U_i. A family of subsets of is called discrete when every point of has a neighbourhood that intersects at most one of the sets from . An equivalent definition demands that the above U_i (i ∈ I) are themselves a discrete family, which is stronger than pairwise disjoint.