Collectionwise Hausdorff space

In mathematics, in the field of topology, a topological space ${\displaystyle X}$ is said to be collectionwise Hausdorff if given any closed discrete subset of ${\displaystyle X}$, 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 ${\displaystyle S\subseteq X}$ being discrete has the usual meaning of being a discrete space with the subspace topology (i.e., all points of ${\displaystyle S}$ are isolated in ${\displaystyle S}$).^{[nb 1]}

Cite error: There are <ref group=nb> tags on this page, but the references will not show without a {{reflist|group=nb}} template (see the help page).