Collectionwise Hausdorff space

In mathematics, in the field of topology, a topological space

is said to be collectionwise Hausdorff if given any closed discrete subset of

, there is a pairwise disjoint family of open sets with each point of the discrete subset contained in exactly one of the open sets.

[1] Here a subset

being discrete has the usual meaning of being a discrete space with the subspace topology (i.e., all points of