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