Collectionwise normal space

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

Definition

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 each is open in their union), there exists a family of pairwise disjoint open sets containing each of the closed sets.

Relation with other properties

Stronger properties

• Metrizable space
• Elastic space
• Linearly orderable space
• Monotonically normal space
• Hereditarily collectionwise normal space

Weaker properties

• Normal space
• Collectionwise Hausdorff space