In mathematics, in the field of topology, a topological space is said to be **collectionwise Hausdorff** if given any closed discrete collection of points in the topological space, there are pairwise disjoint open sets containing the points.^{[1]} A *closed discrete* set *S* of a topology *X* is one where every point of *X* has a neighborhood that intersects at most one point from *S*. Every T1 space which is collectionwise Hausdorff is also Hausdorff.

Metrizable spaces are collectionwise normal spaces and are hence, in particular, collectionwise Hausdorff.

## References

**^**FD Tall, The density topology, Pacific Journal of Mathematics, 1976

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