Collectionwise normal space: Difference between revisions
m (5 revisions) |
|||
| Line 13: | Line 13: | ||
===Stronger properties=== | ===Stronger properties=== | ||
* [[Metrizable space]] | * [[Weaker than::Metrizable space]] | ||
* [[Elastic space]] | * [[Weaker than::Elastic space]] | ||
* [[Linearly orderable space]] | * [[Weaker than::Linearly orderable space]] | ||
* [[Monotonically normal space]] | * [[Weaker than::Monotonically normal space]] | ||
* [[Hereditarily collectionwise normal space]] | * [[Weaker than::Hereditarily collectionwise normal space]] | ||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Normal space]] | * [[Stronger than::Normal space]] | ||
* [[Collectionwise Hausdorff space]] | * [[Stronger than::Collectionwise Hausdorff space]] | ||
Latest revision as of 01:23, 17 January 2009
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