##  [Reach](/reach) 

  ##  [Reach](https://puremath.quantumdictionary.io/reach-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a closed subset A of Euclidean space, the reach is the supremal r≥0 such that every point at distance less than r from A has a unique nearest point in A; equivalently the radius of the largest tubular neighborhood on which the nearest-point projection is well-defined and single-valued.