Collectionwise Hausdorff space

Definition
A topological space is said to be collectionwise Hausdorff if it satisfies the following: it is T1 and given any discrete closed subset (viz a closed subset that is a discrete space under the induced topology), we can find a disjoint family of open sets, with each point of the discrete subset contained in exactly one member open set.

Stronger properties

 * Weaker than::Metrizable space

Weaker properties

 * Stronger than::Hausdorff space: