Normal Hausdorff space: Difference between revisions
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{{topospace property}} | {{topospace property}} | ||
{{T family|T4}} | |||
==Definition== | ==Definition== | ||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[topological space]] is said to be '''normal''' if given any two disjoint [[closed set]]s in the topological space, there are disjoint open sets | A [[topological space]] is said to be '''normal''' if all points in it are closed sets, and given any two disjoint [[closed set]]s in the topological space, there are disjoint open sets containing them. | ||
containing them. | |||
===Definition with symbols=== | ===Definition with symbols=== | ||
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==Relation with other properties== | ==Relation with other properties== | ||
===Stronger properties=== | |||
* [[Compact Hausdorff space]] | |||
* [[Hereditarily normal space]] | |||
* [[Perfectly normal space]] | |||
* [[Metrizable space]] | |||
* [[CW-space]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Completely regular space]] | |||
* [[Regular space]] | |||
* [[Hausdorff space]] | |||
* [[T1 space]] | |||
* [[Kolmogorov space]] | |||
Revision as of 14:26, 22 May 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
In the T family (properties of topological spaces related to separation axioms), this is called: T4
Definition
Symbol-free definition
A topological space is said to be normal if all points in it are closed sets, and given any two disjoint closed sets in the topological space, there are disjoint open sets containing them.
Definition with symbols
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