Collectionwise normal space

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This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of normality. View other variations of normality


Symbol-free definition

A topological space is termed collectionwise normal if it is T1 and, given any discrete collection of closed sets (viz., a disjoint collection of closed sets such that the union of any subcollection is closed), there exists a family of pairwise disjoint open sets containing each of the closed sets.

Relation with other properties

Stronger properties

Weaker properties