Locally normal space: Difference between revisions
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* [[Locally metrizable space]] | * [[Locally metrizable space]] | ||
* [[Normal space]] | * [[Normal space]]: {{proofofstrictimplicationat|[[normal implies locally normal]]|[[locally normal not implies normal]]}} | ||
===Weaker properties=== | ===Weaker properties=== | ||
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==Facts== | ==Facts== | ||
There exist locally normal [[completely regular space]]s that are not [[normal space|normal]]. The classical example is the [[ | There exist locally normal [[completely regular space]]s that are not [[normal space|normal]]. The classical example is the [[Moore plane]]. | ||
Latest revision as of 19:48, 11 May 2008
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
A topological space is termed locally normal if every point in it has an open neighbourhood which is normal.
Relation with other properties
Stronger properties
- Locally metrizable space
- Normal space: For proof of the implication, refer normal implies locally normal and for proof of its strictness (i.e. the reverse implication being false) refer locally normal not implies normal
Weaker properties
Facts
There exist locally normal completely regular spaces that are not normal. The classical example is the Moore plane.