abstract:In mathematics, a topological space X is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊂ Ui. A family \mathcal{F} of subsets of X is called discrete when every point of X has a neighbourhood that intersects at most one of the sets from \mathcal{F}.