##  [Neighborhood System](/neighborhood-system) 

  ##  [Neighborhood System](https://puremath.quantumdictionary.io/neighborhood-system-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An assignment that associates to each point x of a set X a family N(x) of subsets of X called the neighborhoods of x; these families are typically nonempty, each member contains x or at least contains an open set about x, and they are closed under passage to supersets so that any superset of a neighborhood is again a neighborhood.