Collectionwise Hausdorff space
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In mathematics, in the field of topology, a topological space is said to be collectionwise Hausdorff if given any discrete collection of points in the topological space, there are pairwise disjoint open sets containing the points. Every T1 space which is collectionwise Hausdorff is also Hausdorff.
Metrizable spaces are collectionwise normal spaces and are hence, in particular, collectionwise Hausdorff.
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