Refinably normal space: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[topological space]] is termed '''refinably normal''' if it is [[normal space|normal]] and every [[finer topology]] on the space also yields a normal space. Equivalently, it is normal, and every [[dense subset]] is open. | A [[topological space]] is termed '''refinably normal''' if it is [[normal space|normal]] and every [[finer topology]] on the space also yields a normal space. Equivalently, it is normal, and every [[dense subset]] is [[open subset|open]]. | ||
Most normal spaces we encounter in practice are not refinably normal. | Most normal spaces we encounter in practice are not refinably normal. | ||
Revision as of 00:24, 27 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
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Definition
Symbol-free definition
A topological space is termed refinably normal if it is normal and every finer topology on the space also yields a normal space. Equivalently, it is normal, and every dense subset is open.
Most normal spaces we encounter in practice are not refinably normal.