Collectionwise normal space: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A topological space is termed '''collectionwise normal''' if 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. | A topological space is termed '''collectionwise normal''' if it is [[T1 space|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== | ==Relation with other properties== | ||
Revision as of 20:14, 15 December 2007
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.