Collectionwise Hausdorff space: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[topological space]] is said to be '''collectionwise Hausdorff''' if given any discrete subset (viz a subset that is discrete under the induced topology), we can find a disjoint family of open sets, with each point of the discrete subset contained in exactly one member open set. | A [[topological space]] is said to be '''collectionwise Hausdorff''' if given any discrete [[closed subset]] (viz a closed subset that is discrete under the induced topology), we can find a disjoint family of open sets, with each point of the discrete subset contained in exactly one member open set. | ||
===Definition with symbols=== | ===Definition with symbols=== | ||
Revision as of 09:12, 20 August 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 Hausdorffness. View other variations of Hausdorffness
Definition
Symbol-free definition
A topological space is said to be collectionwise Hausdorff if given any discrete closed subset (viz a closed subset that is discrete under the induced topology), we can find a disjoint family of open sets, with each point of the discrete subset contained in exactly one member open set.
Definition with symbols
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