Hereditarily collectionwise normal space

Definition
A topological space is termed hereditarily collectionwise normal or completely collectionwise normal if it satisfies the following two conditions:


 * 1) every subspace of it is collectionwise normal
 * 2) every almost discrete collection of closed subsets can be separated by pairwise disjoint open subsets (here, almost discrete means discrete in the union).

Stronger properties

 * Weaker than::Metrizable space
 * Weaker than::Linearly orderable space
 * Weaker than::Elastic space
 * Weaker than::Monotonically normal space

Weaker properties

 * Stronger than::Collectionwise normal space
 * Stronger than::Hereditarily normal space
 * Stronger than::Normal space
 * Stronger than::Collectionwise Hausdorff space